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Low-orbit satellite internet (LOSI) expands the scope of the Industrial Internet of Things (IIoT) in the oil and gas industry (OGI) to include areas of the Far North. However, due to the large length of the communication channel, the number of threats and attacks increases. A special place among them is occupied by relay spoofing interference. In this case, an intruder satellite intercepts the control signal coming from the satellite (SC), delays it, and then imposes it on the receiver located on the unattended OGI object. This can lead to a disruption of the facility and even cause an environmental disaster. To prevent a spoofing attack, a satellite authentication method has been developed that uses a zero-knowledge authentication protocol (ZKAP). These protocols have high cryptographic strength without the use of encryption. However, they have a significant drawback. This is their low authentication speed, which is caused by calculations over a large module Q (128 bits or more). It is possible to reduce the time of determining the status of an SC by switching to parallel computing. To solve this problem, the paper proposes to use residue codes (RC). Addition, subtraction, and multiplication operations are performed in parallel in RC. Thus, a correct choice of a set of modules of RC allows for providing an operating range of calculations not less than the number Q. Therefore, the development of a spacecraft authentication method for the satellite internet system using RC that allows for reducing the authentication time is an urgent task. [ABSTRACT FROM AUTHOR]

Low-orbit satellite internet (LOSI) expands the scope of the Industrial Internet of Things (IIoT) in the oil and gas industry (OGI) to include areas of the Far North. However, due to the large length of the communication channel, the number of threats and attacks increases. A special place among them is occupied by relay spoofing interference. In this case, an intruder satellite intercepts the control signal coming from the satellite (SC), delays it, and then imposes it on the receiver located on the unattended OGI object. This can lead to a disruption of the facility and even cause an environmental disaster. To prevent a spoofing attack, a satellite authentication method has been developed that uses a zero-knowledge authentication protocol (ZKAP). These protocols have high cryptographic strength without the use of encryption. However, they have a significant drawback. This is their low authentication speed, which is caused by calculations over a large module Q (128 bits or more). It is possible to reduce the time of determining the status of an SC by switching to parallel computing. To solve this problem, the paper proposes to use residue codes (RC). Addition, subtraction, and multiplication operations are performed in parallel in RC. Thus, a correct choice of a set of modules of RC allows for providing an operating range of calculations not less than the number Q. Therefore, the development of a spacecraft authentication method for the satellite internet system using RC that allows for reducing the authentication time is an urgent task.

Let R = ℤ 4 + u ℤ 4 be a finite non-chain ring, where u2 = 1. In this paper, we consider (σ, δ)-skew quasi-cyclic codes over the ring R, where σ is an automorphism of R and δ is an inner σ-derivation of R. We determine the structure of 1-generator (σ, δ)-skew quasi-cyclic codes over R and give a sufficient condition for 1-generator (σ, δ)-skew quasi-cyclic codes over R to be free. We also determine a distance bound for free 1-generator (σ, δ)-skew quasi-cyclic codes. Moreover, using the residue codes of these codes over R we obtain some good ℤ 4 -linear codes. Finally, we give the characterization of Euclidean dual codes of (σ, δ)-skew quasi-cyclic codes. [ABSTRACT FROM AUTHOR]

Motivation Protein–Protein Interactions (PPI) are essentials for most cellular processes and thus, unveiling how proteins interact is a crucial question that can be better understood by identifying which residues are responsible for the interaction. Computational approaches are orders of magnitude cheaper and faster than experimental ones, leading to proliferation of multiple methods aimed to predict which residues belong to the interface of an interaction. Results We present BIPSPI, a new machine learning-based method for the prediction of partner-specific PPI sites. Contrary to most binding site prediction methods, the proposed approach takes into account a pair of interacting proteins rather than a single one in order to predict partner-specific binding sites. BIPSPI has been trained employing sequence-based and structural features from both protein partners of each complex compiled in the Protein–Protein Docking Benchmark version 5.0 and in an additional set independently compiled. Also, a version trained only on sequences has been developed. The performance of our approach has been assessed by a leave-one-out cross-validation over different benchmarks, outperforming state-of-the-art methods. Availability and implementation BIPSPI web server is freely available at http://bipspi.cnb.csic.es. BIPSPI code is available at https://github.com/bioinsilico/BIPSPI. Docker image is available at https://hub.docker.com/r/bioinsilico/bipspi/. Supplementary information Supplementary data are available at Bioinformatics online. [ABSTRACT FROM AUTHOR]

Based on unique decoding of the polynomial residue code with non-pairwise coprime moduli, a polynomial with degree less than that of the least common multiple of all the moduli can be accurately reconstructed when the number of residue errors is less than half the minimum distance of the code. However, once the number of residue errors is beyond half the minimum distance of the code, the unique decoding may fail and lead to a large reconstruction error. In this brief, assuming that all the residues are allowed to have errors with small degrees, we consider how to reconstruct the polynomial as accurately as possible in the sense that a reconstructed polynomial is obtained with only the last ${\tau }$ number of coefficients being possibly erroneous, when the residues are affected by errors with degrees upper bounded by ${\tau }$. In this regard, we first propose a multi-level robust Chinese remainder theorem for polynomials, namely, a tradeoff between the dynamic range of the degree of the polynomial to be reconstructed and the residue error bound ${\tau }$ is formulated. Furthermore, a simple closed-form reconstruction algorithm is also proposed. [ABSTRACT FROM AUTHOR]

For positive integers n, k with 3≤k≤n, let X=F2n\{0,1}, G={{x,x+1}:x∈X}, and Bk={x1,x2,…,xk}⊂X:∑i=1kxi=1,∑i∈Ixi≠1forany∅≠I⫋{1,2,…,k}. Lee et al. used the inclusion-exclusion principle to show that the triple (X,G,Bk) is a (k,λk)-GDD of type 22n-1-1 for k∈{3,4,5,6,7} where λk=∏i=3k-1(2n-2i)(k-2)! (Lee et al. in Des Codes Cryptogr, 10.1007/s10623-017-0395-8, 2017). They conjectured that (X,G,Bk) is also a (k,λk)-GDD of type 22n-1-1 for any integer k≥8. In this paper, we use a similar construction and counting principles to show that there is a (k,λk)-GDD of type (q2-q)(qn-1-1)/(q-1) for any prime power q and any integers k, n with 3≤k≤n where λk=∏i=3k-1(qn-qi)(k-2)!. Consequently, their conjecture holds. Such a method is also generalized to yield a (k,λk)-GDD of type (qℓ+1-qℓ)(qn-ℓ-1)/(q-1) where λk=∏i=3k-1(qn-qℓ+i-1)(k-2)! and k+ℓ≤n+1. [ABSTRACT FROM AUTHOR]

Let 𝔽 p m be the finite field of order p m , where p is an odd prime and m is a positive integer. In this paper, we determine the algebraic structures of all cyclic and negacyclic codes of length 4 p s over the finite commutative chain ring ℛ = 𝔽 p m + u 𝔽 p m , where u 2 = 0 and s is a positive integer. We also obtain the number of codewords in each of these codes. Among others, we establish the duals of all such codes and derive some self-dual cyclic and negacyclic codes of length 4 p s over ℛ. [ABSTRACT FROM AUTHOR]

The projective special linear group ${\mathrm {PSL}}_{2}(n)$ is 2-transitive for all primes $n$ and 3-homogeneous for $n \equiv 3 \pmod {4}$ on the set $\{0,1, \ldots, n-1, \infty \}$. It is known that the extended odd-like quadratic residue codes are invariant under ${\mathrm {PSL}}_{2}(n)$. Hence, the extended quadratic residue codes hold an infinite family of 2-designs for primes $n \equiv 1 \pmod {4}$ , an infinite family of 3-designs for primes $n \equiv 3 \pmod {4}$. To construct more $t$ -designs with $t \in \{2, 3\}$ , one would search for other extended cyclic codes over finite fields that are invariant under the action of ${\mathrm {PSL}}_{2}(n)$. The objective of this paper is to prove that the extended quadratic residue binary codes are the only nontrivial extended binary cyclic codes that are invariant under ${\mathrm {PSL}}_{2}(n)$. [ABSTRACT FROM AUTHOR]

Mobile adhoc network (MANET) possesses various security challenges mainly due to its varying network topology. As central coordination is not possible in MANETs, sharing of keys between nodes is a difficult task. In this paper, we present a Binary Hex Quadratic Residue Security Model that does not require any kind of key distribution between the nodes in MANETs. We use a stream of equal weighted hex codes of decimal numbers and Ex-OR operations to generate a security vector which facilitates matching of code words and also determine the active and malicious nodes in the network. Our approach also saves energy as it requires less computational analysis when compared to existing approaches. We validate our approach through simulations results. [ABSTRACT FROM AUTHOR]

In this paper, an efficient decoding algorithm is developed to facilitate faster decoding of the binary systematic quadratic residue (QR) codes. It is based on the difference of syndromes (DS), and hence, is called the DS algorithm hereinafter. This new method combines the advantages of the syndrome-weight algorithm and properties of the cyclic codes. Actually, it is a natural generalization of the cyclic weight (CW) algorithm for the (47, 24, 11) QR code developed by Lin et al., and its validity of decoding any binary systematic QR code is also proved. The complexity analysis and simulation results show that the DS algorithm dramatically reduces the decoding complexity without performance loss and considerably requires less memory when compared with previous ones. Utilizing the (47, 24, 11), the (71, 36, 11), the (73, 37, 13), and the (89, 45, 17) QR codes as examples, the DS algorithm not only significantly improves the decoding efficiency, but also saves the memory evidently. When the (23, 12, 7) QR code is considered, the DS algorithm performs almost as well as the currently known best algorithm in terms of decoding efficiency and memory requirements. Thus, all QR codes of lengths less than 100 can be decoded efficiently by using the proposed algorithm. Especially, when the proposed algorithm is applied to decode the (89, 45, 17) QR code, the best one among all the QR codes of lengths less than 100, the decoding speed is raised 26 times and the memory is saved up to 76.6% in comparison with the existing fastest decoding algorithm. [ABSTRACT FROM AUTHOR]

This paper gives a construction of group divisible designs (GDDs) on the binary extension fields with block sizes 3, 4, 5, 6, and 7, respectively, which consist of the error patterns whose first syndromes are zeros recognized from the decoding of binary quadratic residue codes. A conjecture is proposed for this construction of GDDs with larger block sizes. [ABSTRACT FROM AUTHOR]

We construct an even extremal lattice of rank 64 by means of a generalized quadratic residue code. [ABSTRACT FROM AUTHOR]

Authenticated key exchange protocols represent an important cryptographic mechanism that enables several parties to communicate securely over an open network. Elashry, Mu, and Susilo proposed an identity-based authenticated key exchange (IBAKE) protocol where different parties establish secure communication by means of their public identities.The authors also introduced a new security notion for IBAKE protocols called resiliency, that is, if the secret shared key is compromised, the entities can generate another shared secret key without establishing a new session between them. They then claimed that their IBAKE protocol satisfies this security notion. We analyze the security of their protocol and prove that it has a major security flaw, which renders it insecure against an impersonation attack. We also disprove the resiliency property of their scheme by proposing an attack where an adversary can compute any shared secret key if just one secret bit is leaked. [ABSTRACT FROM AUTHOR]

We identify a transfer method from bounded existentially quantified Diophantine equations to formulas of Tarski algebra, the first order theory of the real field. The method is applied to show that NP is contained in ⋃ n = 1 ∞ Dtime ( 2 a ⋅ log O ( 1 ) n ) , where a depends only on the given Diophantine equation. [ABSTRACT FROM AUTHOR]

We investigate Steiner's Porism in finite MiquelianMöbius planes constructed over the pair of finite fields GF(q) and GF(q²), for an odd prime power q. Properties of common tangent circles for two given concentric circles are discussed and with that, a finite version of Steiner's Porism for concentric circles is stated and proved. We formulate conditions on the length of a Steiner chain by using the quadratic residue theorem in GF(q). These results are then generalized to an arbitrary pair of non-intersecting circles by introducing the notion of capacitance, which turns out to be invariant under Möbius transformations. Finally, the results are compared with the situation in the classical Euclidean plane. [ABSTRACT FROM AUTHOR]

In this research-based experiment, students are introduced to the interdisciplinary field of archaeological chemistry by extracting and analyzing lipid residues absorbed in pottery. Reproduction archaeological pottery sherds are prepared by soaking ceramic fragments in individual or combinations of vegetable oils. Students crush and extract the absorbed residues, transesterify the recovered lipids to fatty acid methyl esters, and analyze the product by GC or GC/MS. Recovered residues are characterized by analysis of the major fatty acid peaks, as identified using reference standards or mass spectral databases. An archaeological context that links the sherds to the Minoan civilization is provided to students and must be considered to correctly identify the absorbed residue(s). The laboratory has been used in a topical archaeological instrumentation course that has attracted second to fourth year students majoring in chemistry, biochemistry, and anthropology, and museum studies minors. Pedagogically, the laboratory introduces students to techniques currently used in the field of archaeological chemistry while reinforcing fundamental concepts in sample isolation and preparation, derivatization, gas chromatography, mass spectrometry, and multicomponent sample analysis. [ABSTRACT FROM AUTHOR]

We introduce a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding. Rather than relying on the precise structure of the codes, our method exploits code symmetry. In particular, the technique applies to any sequence of linear codes where the blocklengths are strictly increasing, the code rates converge, and the permutation group of each code is doubly transitive. In other words, we show that symmetry alone implies near-optimal performance. An important consequence of this result is that a sequence of Reed–Muller codes with increasing blocklength and converging rate achieves capacity. This possibility has been suggested previously in the literature but it has only been proven for cases where the limiting code rate is 0 or 1. Moreover, these results extend naturally to all affine-invariant codes and, thus, to extended primitive narrow-sense BCH codes. This also resolves, in the affirmative, the existence question for capacity-achieving sequences of binary cyclic codes. The primary tools used in the proof are the sharp threshold property for symmetric monotone Boolean functions and the area theorem for extrinsic information transfer functions. [ABSTRACT FROM PUBLISHER]

Quadratic residue (QR) codes and their extensions over the finite non-chain ring are studied, where , is an odd prime and . A class of Gray maps preserving the self-duality of linear codes from to is given. Under a special Gray map, a self-dual code over , a formally self-dual code over and a formally self-dual code over are obtained from extended QR codes. [ABSTRACT FROM AUTHOR]

The study of frequency-hopping sequences (FHSs) has been focused on the establishment of theoretical bounds for the parameters of FHSs as well as on the construction of optimal FHSs with respect to the bounds. Peng and Fan (IEEE Trans Inf Theory 50(9):2149-2154, 2004) derived two lower bounds on the maximum nontrivial Hamming correlation of an FHS set, which is an important indicator in measuring the performance of an FHS set employed in practice. In this paper, we obtain two main results. We study the construction of new optimal frequency-hopping sequence sets by using cyclic codes over finite fields. Let $$\mathcal {C}$$ be a cyclic code of length n over a finite field $$\mathbb {F}_q$$ such that $$\mathcal {C}$$ contains the one-dimensional subcode $$ \mathcal {C}_0=\{(\alpha ,\alpha ,\ldots ,\alpha )\in \mathbb {F}_q^n\,|\,\alpha \in \mathbb {F}_q\}. $$ Two codewords of $$\mathcal {C}$$ are said to be equivalent if one can be obtained from the other through applying the cyclic shift a certain number of times. We present a necessary and sufficient condition under which the equivalence class of any codeword in $$\mathcal {C}\setminus \mathcal {C}_0$$ has size n. This result addresses an open question raised by Ding et al. (IEEE Trans Inf Theory 55(7):3297-3304, 2009). As a consequence, three new classes of optimal FHS sets with respect to the Singleton bound are obtained, some of which are also optimal with respect to the Peng-Fan bound at the same time. We also show that the two Peng-Fan bounds are, in fact, identical. [ABSTRACT FROM AUTHOR]

The depth spectrum of any negacyclic code over Z 4 of even length is completely determined by using its residue and torsion codes. [ABSTRACT FROM AUTHOR]

We propose a new display system technology that can hide secret information behind a displayed image, while simultaneously satisfying both high invisibility and readability requirements. The hidden information is a kind of binary image including characters, and various kinds of patterns, i.e., quadratic residue (QR) codes. This technique uses a temporally bright modulated invisible pattern in a moving image, or video. Frame images over some periods are summed up when read out, enhancing the contrast of the invisible pattern to make it visible. We also propose a new method to solve an issue that occurs due to asynchronous operations of the display and video camera, which is a technique that was achieved by using time-shift sampling. The hidden binary image could be read out according to experiments that we conducted to confirm the results. Moreover, the patterns used in this technique were decidedly invisible when laid behind the main images, which suggested the proposed technique was highly feasible in practical applications according to this confirmation. [ABSTRACT FROM AUTHOR]

In a recent study, Li et al. proposed an algorithm for the decoding of binary quadratic residue codes with tiny memory requirements. In this Letter, this algorithm is modified in order to dramatically improve the decoding speed. The case of the (89,45,17) binary quadratic residue code is used to illustrate the new algorithm. [ABSTRACT FROM AUTHOR]

In this article, we show explicitly all possible weight enumerators for every irreducible cyclic code of length $$n$$ over a finite field $${\mathbb {F}}_q$$ , in the case which each prime divisor of $$n$$ is also a divisor of $$q-1$$ . [ABSTRACT FROM AUTHOR]

Over the past few years, secure and privacy-preserving user authentication scheme has become an integral part of the applications of the healthcare systems. Recently, Wen has designed an improved user authentication system over the Lee et al.’s scheme for integrated electronic patient record (EPR) information system, which has been analyzed in this study. We have found that Wen’s scheme still has the following inefficiencies: (1) the correctness of identity and password are not verified during the login and password change phases; (2) it is vulnerable to impersonation attack and privileged-insider attack; (3) it is designed without the revocation of lost/stolen smart card; (4) the explicit key confirmation and the no key control properties are absent, and (5) user cannot update his/her password without the help of server and secure channel. Then we aimed to propose an enhanced two-factor user authentication system based on the intractable assumption of the quadratic residue problem (QRP) in the multiplicative group. Our scheme bears more securities and functionalities than other schemes found in the literature. [ABSTRACT FROM AUTHOR]

Quadratic residue codes are a well-known class of codes. In this paper, we consider the constructions of self-dual codes by higher power residues, especially fourth power residues. New infinite families of self-dual codes over GF(2), GF(3), GF(4), GF(8), and GF(9) are introduced. Some of them have better minimum weight than previously known codes. We also give general results related to the automorphism group of some of these codes. [ABSTRACT FROM PUBLISHER]

We prove that the only primes which may divide the order of the automorphism group of a putative binary self-dual doubly-even [120, 60, 24] code are 2, 3, 5, 7, 19, 23 and 29. Furthermore we prove that automorphisms of prime order p ≥ 5 have a unique cycle structure. Parts of the results are based on computer computations. [ABSTRACT FROM AUTHOR]

There are several methods for constructing self-dual codes over various rings. Among them, the building-up method is a powerful method, and it can be applied to self-dual codes over finite fields and several rings. Recently, Alfaro and Dhul-Qarnayn (Des Codes Cryptogr, doi:10.1007/s10623-013-9873-9) proposed a method for constructing self-dual codes over Fq[u]/(ut. Their approach is a building-up approach that uses the matrix form. In this paper, we use the matrix form to develop a building-up approach for constructing self-dual codes over Z2m} (m ≥ 1), which have not been considered thus far. [ABSTRACT FROM AUTHOR]

A class of powerful $$q$$ -ary linear polynomial codes originally proposed by Xing and Ling is deployed to construct good asymmetric quantum codes via the standard CSS construction. Our quantum codes are $$q$$ -ary block codes that encode $$k$$ qudits of quantum information into $$n$$ qudits and correct up to $$\left\lfloor (d_{x}-1)/2 \right\rfloor $$ bit-flip errors and up to $$\left\lfloor (d_{z}-1)/2 \right\rfloor $$ phase-flip errors. In many cases where the length $$(q^{2}-q)/2 \le n \le (q^{2}+q)/2$$ and the field size $$q$$ are fixed and for chosen values of $$d_{x} \in \{2,3,4,5\}$$ and $$d_{z} \ge \delta $$ , where $$\delta $$ is the designed distance of the Xing-Ling (XL) codes, the derived pure $$q$$ -ary asymmetric quantum CSS codes possess the best possible size given the current state of the art knowledge on the best classical linear block codes. [ABSTRACT FROM AUTHOR]

This paper investigates polynomial remainder codes with non-pairwise coprime moduli. We first consider a robust reconstruction problem for polynomials from erroneous residues when the degrees of all residue errors are assumed small, namely, the robust Chinese Remainder Theorem (CRT) for polynomials. It basically says that a polynomial can be reconstructed from its erroneous residues such that the degree of the reconstruction error is upper bounded by $\tau$ whenever the degrees of all residue errors are upper bounded by $\tau$, where a sufficient condition for $\tau$ and a reconstruction algorithm are obtained. By relaxing the constraint that all residue errors have small degrees, another robust reconstruction is then presented when there are multiple unrestricted errors and an arbitrary number of errors with small degrees in the residues. We finally obtain a stronger residue error correction capability in the sense that apart from the number of errors that can be corrected in the previous existing result, some errors with small degrees can be also corrected in the residues. With this newly obtained result, improvements in uncorrected error probability and burst error correction capability in data transmission are illustrated. [ABSTRACT FROM PUBLISHER]

In this paper, an explicit expression of the weak-locator polynomial for $p$ -ary quadratic residue codes is presented by a modification of the Feng–Tzeng matrix method. The differences between the modified version and the original Feng–Tzeng matrix are that in the new matrix, not every entry is a syndrome, and every syndrome entry is a known syndrome. By utilizing this technique, an algebraic decoding of the ternary (61, 30, 12) quadratic residue code is proposed. This new result has never been seen in the literature to our knowledge. An advantage of the proposed decoding algorithm is that in general the obtained weak-locator polynomials can decode efficiently not only all the error patterns of weights four and five, but also some error patterns of weight six. [ABSTRACT FROM PUBLISHER]

The WSN standard IEEE802.15.4 basically uses the unlicensed frequency of 2,4 GHz for data transmission in a variety of devices, standards and applications: IEEE802.11, Bluetooth and etc. In this paper we proposed modified correction codes -- based on Residue Number System -- to improve the data transmission robustness in WSN. These codes are characterized by high correction characteristics as well as the simplified coding procedure. There are given examples, and circuits of the both coder and decoder are designed for such modified correction codes using the Residue Number System and CPLD. [ABSTRACT FROM AUTHOR]

In this note, we demonstrate that every binary doubly even self-dual code of length 40 can be realized as the residue code of some extremal Type II Z 4 -code. As a consequence, it is shown that there are at least 94356 inequivalent extremal Type II Z 4 -codes of length 40 . [ABSTRACT FROM AUTHOR]

Abstract: In this paper quadratic residue codes over the ring are introduced in terms of their idempotent generators. The structure of these codes is studied and it is observed that these codes enjoy similar properties as quadratic residue codes over finite fields. For the case , Euclidean and Hermitian self-dual families of codes as extended quadratic residue codes are considered and two optimal Hermitian self-dual codes are obtained as examples. Moreover, a substantial number of good p-ary codes are obtained as images of quadratic residue codes over in the cases where p is an odd prime. These results are presented in tables. [Copyright &y& Elsevier]

In this work, quadratic residue codes over the ring F 2 + u F 2 + u 2 F 2 with u 3 = u are considered. A duality and distance preserving Gray map from F 2 + u F 2 + u 2 F 2 to F 2 3 is defined. By using quadratic double circulant, quadratic bordered double circulant constructions and their extensions self-dual codes of different lengths are obtained. As Gray images of these codes and their extensions, a substantial number of new extremal self-dual binary codes are found. More precisely, thirty two new extremal binary self-dual codes of length 68, 363 Type I codes of parameters [ 72 , 36 , 12 ] , a Type II [ 72 , 36 , 12 ] code and a Type II [ 96 , 48 , 16 ] code with new weight enumerators are obtained through these constructions. The results are tabulated. [ABSTRACT FROM AUTHOR]

Let $$D$$ be the support design of the minimum weight of an extremal binary doubly even self-dual $$[24m,12m,4m+4]$$ code. In this note, we consider the case when $$D$$ becomes a $$t$$-design with $$t \ge 6$$. [ABSTRACT FROM AUTHOR]

In this paper, a new class of (N,K) near-optimal partial Hadamard codebooks is proposed. The construction of the proposed codebooks from Hadamard matrices is based on binary row selection sequences, which are generated by quadratic residue mapping of p -ary m -sequences. The proposed codebooks have parameters and K=({p-1}/{2p})(N+\sqrt{N})+1 for an odd prime p$ and an even positive integer $n$ . We prove that the maximum magnitude of inner products between the code vectors of the proposed codebooks asymptotically achieves the Welch bound equality for sufficiently large $p$ and derive their inner product distribution. [ABSTRACT FROM PUBLISHER]

Recently, the unified unknown syndrome representations to decode a class of binary cyclic codes have been developed by using Lagrange interpolation formula (discussed by Chang and Lee in 2010). In this study, a new method by combining the syndrome matrix search and modified Chinese remainder theorem is proposed to express the unified unknown syndrome representation as a rational function in terms of the known syndromes. A computer simulation has been executed to determine the syndrome matrices for binary cyclic codes of lengths less than or equal to 51. Compared to the Lagrange interpolation method, the method presented here substantially reduces the computational time for binary cyclic codes generated by irreducible polynomials. Finally, a complete decoding of the (31, 16, 7) quadratic residue code with inverse-free Berlekamp-Massey algorithm is given as an illustration. [ABSTRACT FROM AUTHOR]

A set M ⊆ E is called an acyclic matching of a graph G = (V, E) if no two edges in M are adjacent and the subgraph induced by the set of end vertices of the edges of M is acyclic. Given a positive integer k and a graph G = (V, E), the acyclic matching problem is to decide whether G has an acyclic matching of cardinality at least k. Goddard et al. ( Discrete Math. 293(1-3) (2005) 129-138) introduced the concept of the acyclic matching problem and proved that the acyclic matching problem is NP-complete for general graphs. In this paper, we propose an O(n + m) time algorithm to find a maximum cardinality acyclic matching in a chain graph having n vertices and m edges and obtain an expression for the number of maximum cardinality acyclic matchings in a chain graph. We also propose a dynamic programming-based O(n + m) time algorithm to find a maximum cardinality acyclic matching in a bipartite permutation graph having n vertices and m edges. Finally, we strengthen the complexity result of the acyclic matching problem by showing that this problem remains NP-complete for perfect elimination bipartite graphs. [ABSTRACT FROM AUTHOR]

This paper presents some results on multiple error detection and correction based on the Redundant Residue Number System (RRNS). RRNS is often used in parallel processing environments because of its ability to increase the robustness of information passing between the processors. The proposed multiple error correction scheme utilizes the Chinese Remainder Theorem (CRT) together with a novel algorithm that significantly simplifies the error correcting process for integers. An extension of the scheme further reduces the computational complexity without compromising its error correcting capability. Proofs and examples are provided for the coding technique. [ABSTRACT FROM AUTHOR]

We present a novel symbol-based soft-input a posteriori probability (APP) decoder for packetized variable-length encoded source indexes transmitted over wireless channels where the residual redundancy after source encoding is exploited for error protection. In combination with a mean-square or maximum APP estimation of the reconstructed source data, the whole decoding process is close to optimal. Furthermore, solutions for the proposed APP decoder with reduced complexity are discussed and compared to the near-optimal solution. When, in addition, channel codes are employed for protecting the variable-length encoded data, an iterative source-channel decoder can be obtained in the same way as for serially concatenated codes, where the proposed APP source decoder then represents one of the two constituent decoders. The simulation results show that this iterative decoding technique leads to substantial error protection for variable-length encoded correlated source signals, especially, when they are transmitted over highly corrupted channels. [ABSTRACT FROM PUBLISHER]

Motivation: Previously, we developed a computational model to identify genomic co-occurrence networks that was applied to capture the coevolution patterns within genomes of influenza viruses. To facilitate easy public use of this model, an R package 'cooccurNet' is presented here. Results: 'cooccurNet' includes functionalities of construction and analysis of residues (e.g. nucleotides, amino acids and SNPs) co-occurrence network. In addition, a new method for measuring residues coevolution, defined as residue co-occurrence score (RCOS), is proposed and implemented in 'cooccurNet' based on the co-occurrence network. [ABSTRACT FROM AUTHOR]

A response from the author of the article "On Decoding of the (89, 45, 17) Quadratic Residue Code" that was published in a previous issue is presented and also mentions required correction on the same article.