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In this article, we describe two classes of few-weight ternary codes, compute their minimum weight and weight distribution from mathematical objects called simplicial complexes. One class of codes described here has the same parameters with the binary first-order Reed-Muller codes. A class of (optimal) minimal linear codes is also obtained in this correspondence.

A computational approach to using plug-in arrays, circulant matrices, and negacirculant matrices in the construction and enumeration of extremal and near-extremal self-dual ternary codes. Isomorphism classes of such codes obtainable from orthogonal designs of dimensions 2, 4, and 8 are completely enumerated for several lengths. Additionally, partial searches are conducted for larger lengths, and weight enumerators are derived for near-extremal codes. [ABSTRACT FROM AUTHOR]

Linear codes over finite fields are one of the most well-studied areas in coding theory. While codes over finite fields of characteristic two are of particular practical interest due to their good implementation properties, ternary codes have been extensively studied as well. By contrast, there has been essentially no research into ternary cryptographic algorithms. The only exception to date is a cryptocurrency and distributed ledger technology called IOTA which is ternary and has been designed primarily for use in the Internet of Things. Its security depends on using a secure cryptographic hash function over F 3 . With all existing hash designs being binary, a ternary prototype called Curl-P had been developed, however was found to admit practical collision attacks. A ternary adaption of SHA-3 called Kerl is currently used instead, but comparatively inefficient. In this paper, we propose a new ternary hash function called Troika which is tailored for use in IOTA's ternary distributed ledger and can be used as a drop-in replacement for Kerl. The design of Troika leverages elements from the well-established Keccak and Rijndael design philosophies, while being designed for efficiency in terms of basic F 3 operations. In particular, it features a novel 3-trit S-box which is differentially 3-uniform while being implementable in only 7 additions and multiplications over F 3 . Troika is designed to offer a security level comparable to SHA-3. It is expected that Troika, as part of IOTA's distributed ledger, will find widespread commercial real-world use in the near- to mid-term future. We believe that not the least due to its unorthodox ternary design, it will provide both a practically relevant and interesting target for further cryptanalysis. [ABSTRACT FROM AUTHOR]

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems and communication systems as they have efficient encoding and decoding algorithms. In 2013, Ding, et al. presented nine open problems about optimal ternary cyclic codes. The first two and the 6th problems were completely solved, and the third and last three problems were partially solved. In this paper, we focus on the 7th problem. By determining the root set of some special polynomials over finite fields, we give an incomplete answer and then present a counterexample. Furthermore, we construct two new classes of optimal ternary cyclic codes with respect to the Sphere Packing Bound by studying some special polynomials over finite fields. [ABSTRACT FROM AUTHOR]

It is known that, for large user word lengths, the auxiliary data can be used to recover most of the redundancy losses of Knuth’s simple balancing method compared with the optimal redundancy of balanced codes for the binary case. Here, this important result is extended in a number of ways. First, an upper bound for the amount of auxiliary data is derived that is valid for all codeword lengths. This result is primarily of theoretical interest, as it defines the probability distribution of the number of balancing indices that results in optimal redundancy. This result is equally valid for particular non-binary generalizations of Knuth’s balancing method. Second, an asymptotically exact expression for the amount of auxiliary data for the ternary case of a variable length realization of the modified balanced code construction is derived, that, in all respects, is the analogue of the result obtained for the binary case. The derivation is based on a generalization of the binary random walk to the ternary case and a simple modification of an existing generalization of Knuth’s method for the non-binary balanced codes. Finally, a conjecture is proposed regarding the probability distribution of the number of balancing indices for any alphabet size. [ABSTRACT FROM AUTHOR]

Linear codes with a few weights have applications in data storage systems, secret sharing schemes, and authentication codes. Recently, Ding (IEEE Trans. Inf. Theory 61(6):3265-3275, 2015) proposed a class of ternary linear codes with three weights from a family of cyclic difference sets in (F3m∗/F3∗,×), where m=3k and k is odd. One objective of this paper is to construct ternary linear codes with three weights from cyclic difference sets in (F3m∗/F3∗,×) derived from the Helleseth-Gong functions. This construction works for any positive integer m=sk with an odd factor s≥3, and thus leads to three-weight ternary linear codes with more flexible parameters than earlier ones mentioned above. Another objective of this paper is to determine the weight distribution of the proposed linear codes. [ABSTRACT FROM AUTHOR]

The punctured binary Reed–Muller code is cyclic and was generalised into the punctured generalised Reed–Muller code over GF ( q ) in the literature. The first objective of this paper is to present another generalisation of the punctured binary Reed–Muller code and the binary Reed–Muller code, and analyse these codes. The second objective of this paper is to consider two applications of the new codes in constructing LCD codes and 2-designs. The major motivation of constructing and studying the new codes and their extended codes is the construction of 2-designs, which is an interesting topic in combinatorics. It is remarkable that the family of newly generalised cyclic codes contains a subclass of optimal ternary codes with parameters [ 3 m − 1 , 3 m − 1 − 2 m , 4 ] for all m ≥ 2 . Their extended codes have parameters [ 3 m , 3 m − 1 − 2 m , 5 ] for all m ≥ 2 , and are also optimal. [ABSTRACT FROM AUTHOR]

In this work, we investigated the effect of boron addition on glass-forming ability and mechanical properties of Co-Cr-Mo-C alloys. The starting alloy was (Co 0.65 Cr 0.13 Mo 0.22 ) 80 C 20 derived from the Co 65 Cr 13 Mo 22 ternary eutectic composition. This alloy is almost fully crystalline and exhibits brittle mechanical properties. Replacing carbon with boron allows obtaining bulk metallic glasses (BMGs) and bulk metallic glass composites. The designed alloys show very high strength (∼4100 MPa), wide super-cooled liquid region (∼100 K) and large endothermic enthalpy of the supercooled liquid region (∼35 J/g), indicating high thermal stability. The electronegativity difference and supercooled liquid region of the present alloys are comparable to rare-earth elements containing BMGs. The physical properties of the present alloys corresponded well with the alloy design strategy based on the unified parameter using the glass transition temperature, fracture strength, and molar volume. Furthermore, we propose the optimum compositional condition for glass formation by controlling the carbon-to-boron ratio and the influence of carbon on phase formation in this alloy system is discussed. [ABSTRACT FROM AUTHOR]

For nonnegative integers n 2 , n 3 and d , let N ( n 2 , n 3 , d ) denote the maximum cardinality of a code of length n 2 + n 3 , with n 2 binary coordinates and n 3 ternary coordinates (in this order) and with minimum distance at least d . For a nonnegative integer k , let C k denote the collection of codes of cardinality at most k . For D ∈ C k , define S ( D ) ≔ { C ∈ C k ∣ D ⊆ C , | D | + 2 | C ∖ D | ≤ k } . Then N ( n 2 , n 3 , d ) is upper bounded by the maximum value of ∑ v ∈ [ 2 ] n 2 [ 3 ] n 3 x ( { v } ) , where x is a function C k → R such that x ( ∅ ) = 1 and x ( C ) = 0 if C has minimum distance less than d , and such that the S ( D ) × S ( D ) matrix ( x ( C ∪ C ′ ) ) C , C ′ ∈ S ( D ) is positive semidefinite for each D ∈ C k . By exploiting symmetry, the semidefinite programming problem for the case k = 3 is reduced using representation theory. It yields 135 new upper bounds that are provided in tables. [ABSTRACT FROM AUTHOR]

In recent years, image sharpening detection has become one of the main topics in the field of image forensics. It is, however, still a challenge to detect the images sharpened with weak sharpening strength. To address this challenge, we propose an efficient method for image sharpening detection. In the proposed method, a ternary coding strategy with adaptive threshold is introduced to reveal the overshoot artifacts caused by weak sharpening. Extensive experiments are conducted to illustrate the superiority of the proposed method. The experimental results show that the proposed method can achieve a considerable improvement in sharpening detection, especially for slightly sharpened images. [ABSTRACT FROM AUTHOR]

We give a classification of ternary maximal self-orthogonal codes of lengths 21; 22 and 23. This completes a classification of ternary maximal self-orthogonal codes of lengths up to 24. [ABSTRACT FROM AUTHOR]

The Nb-Si-Ta ternary system is thermodynamically assessed using the CALculation of PHAse Diagram approach based on the experimental measurements of the isothermal sections at 1100, 1200, and 1300 °C. The parameters for the thermodynamic assessment of all the phases in the system are optimized, following the reported literatures of the three relevant binaries Nb-Si, Nb-Ta and Si-Ta systems. The liquidus projection was calculated accordingly from the currently obtained thermodynamic description of the Nb-Si-Ta system. Comparison between the calculated results and the experimental investigations shows that the present modeling can finely describe the experimental information of the Nb-Si-Ta ternary phase diagram. [ABSTRACT FROM AUTHOR]

We study codes with parameters of the ternary Hamming (n = (3 m − 1) / 2 , 3 n − m , 3) code, i.e., ternary 1-perfect codes. The rank of the code is defined to be the dimension of its affine span. We characterize ternary 1-perfect codes of rank n − m + 1 , count their number, and prove that all such codes can be obtained from each other by a sequence of two-coordinate switchings. We enumerate ternary 1-perfect codes of length 13 obtained by concatenation from codes of lengths 9 and 4; we find that there are 93241327 equivalence classes of such codes. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the pulse amplitude modulation (PAM) decomposition and the spectral efficiency of duobinary continuous phase modulation (CPM), where duo- binary CPM represents a ternary CPM whose symbols are generated using a duobinary encoder. We show that this precoder ensures a higher spectral efficiency compared with binary CPM and we propose a PAM decomposition characterized by the presence of a single main pulse and by uncorrelated pseudo-symbols for a half integer modulation index value for this ternary CPM. We show that shaped offset quadrature phase shift keying belongs to this CPM family and we provide a new reduced complexity trellis detector capable of reaching identical performance as the one introduced by Perrins as well as new linear detectors. [ABSTRACT FROM AUTHOR]

We show that there are exactly 4285 symmetric (45,12,3) designs that admit nontrivial automorphisms. Among them there are 1161 self-dual designs and 1562 pairs of mutually dual designs. We describe the full automorphism groups of these designs and analyze their ternary codes. R. Mathon and E. Spence have constructed 1136 symmetric (45,12,3) designs with trivial automorphism group, which means that there are at least 5421 symmetric (45,12,3) designs. Further, we discuss trigeodetic graphs obtained from the symmetric (45; 12; 3) designs. We prove that k-geodetic graphs constructed from mutually non-isomorphic designs are mutually non-isomorphic, hence there are at least 5421 mutually non-isomorphic trigeodetic graphs obtained from symmetric (45; 12; 3) designs. [ABSTRACT FROM AUTHOR]

Production of formic acid (FA) by hydrogenation of CO2 using a ternary hybrid catalyst, poly(ethyleneimine)-tethered Ir-iminophosphine complex (Ir-PN-PEI) immobilized in titanate nanotubes (TNTs), is reported. On the basis of comprehensive structural analyses, we show that Ir-PN-PEI is tightly immobilized within the cavity space of TNT without affecting the electronic/coordination states of Ir atoms. Liquid-phase CO2 hydrogenation under pressurized CO2 and H2 demonstrates that the Ir-PN-PEI catalyst immobilized in Na+-type TNT exhibits the highest FA yields (TON>1000 for 20 h under mild reaction conditions (2.0 MPa, 140 °C)) and improved reusability, which far outperform those of unimmobilized prototype Ir-PN-PEI. The improved catalytic performance is attributed to the ability of TNT to efficiently capture CO2 and to stabilize PEI, with Na+-type TNT with higher basic property providing a more productive effect. The catalyst is reusable over multiple cycles with activity comparable to those of heterogeneous catalysts previously reported, rendering this material suitable for efficient transformation of CO2 into FA. [ABSTRACT FROM AUTHOR]

Lattices are discrete mathematical objects with widespread applications to integer programs as well as modern cryptography. An important class of lattices are those that possess an orthogonal basis, since if such an orthogonal basis is known, then many other fundamental problems on lattices can be solved easily (e.g., the Closest Vector Problem). However, intriguingly, deciding whether a lattice has an orthogonal basis is not known to be either NP-complete or in P. In this paper, we focus on the orthogonality decision problem for a well-known family of lattices, namely Construction-A lattices. These are lattices of the form C + qℤn, where C is an error-correcting q-ary code, and are studied in communication settings. We provide a complete characterization of lattices obtained from binary and ternary codes using Construction-A that have an orthogonal basis. We use this characterization to give an efficient algorithm to solve the orthogonality decision problem. Our algorithm also finds an orthogonal basis if one exists for this family of lattices. [ABSTRACT FROM AUTHOR]

A ternary [ 66 , 10 , 36 ] 3 -code admitting the Mathieu group M 12 as a group of automorphisms has recently been constructed by N. Pace, see Pace (2014). We give a construction of the Pace code in terms of M 12 as well as a combinatorial description in terms of the small Witt design, the Steiner system S ( 5 , 6 , 12 ) . We also present a proof that the Pace code does indeed have minimum distance 36 . [ABSTRACT FROM AUTHOR]

Two-weight linear codes have many wide applications in authentication codes, association schemes, strongly regular graphs, and secret sharing schemes. In this paper, we present two classes of two-weight binary or ternary linear codes. In some cases, they are optimal or almost optimal. They can also be used to construct secret sharing schemes. [ABSTRACT FROM AUTHOR]

Recently, ithas been observed that {0,±1}‐ternary codes, which are simply generated from deep features by hard thresholding, tend to outperform {−1,1}‐binary codes in image retrieval. To obtain better ternary codes, the authors for the first time propose to jointly learn the features with the codes by appending a smoothed function to the networks. During training, the function could evolve into a non‐smoothed ternary function by a continuation method, and then generate ternary codes. The method circumvents the difficulty of directly training discrete functions and reduces the quantization errors of ternary codes. Experiments show that the proposed joint learning indeed could produce better ternary codes. For the first time, the authors propose to generate ternary hash codes by jointly learning the codes with deep features via a continuation method. Experiments show that the proposed method outperforms existing methods. [ABSTRACT FROM AUTHOR]

Let [n, k, d]q code be a linear code of length n, dimension k and minimum Hamming distance d over GF(q). One of the basic and most important problems in coding theory is to construct codes with best possible minimum distances. In this paper seven quasi-twisted ternary linear codes are constructed. These codes are new and improve the best known lower bounds on the minimum distance in [6]. [ABSTRACT FROM AUTHOR]

The sizes of optimal constant-composition codes of weight three have been determined by Chee, Ge and Ling with four cases in doubt. Group divisible codes played an important role in their constructions. In this paper, we study the problem of constructing optimal ternary constant-composition codes with Hamming weight four and minimum distance six. The problem is solved with a small number of lengths undetermined. The previously known results are those with code length no greater than 10. [ABSTRACT FROM AUTHOR]

Deep packet inspection in modern networking and security devices use ternary content addressable memory (TCAM) to match regular expressions. TCAM has its advantage in search speed but disadvantages in limited storage and high power consumption. The hierarchical encoding algorithm to save TCAM space is proposed and the codes divided into four layers. The proposal and the results are tested showing that the new algorithm has higher compression efficiency and the compression rate can reach 95–99%. [ABSTRACT FROM AUTHOR]

We examine the ternary codes $$C_3(A_i+I)$$ from matrices $$A_i+I$$ where $$A_i$$ is an adjacency matrix of a uniform subset graph $$\Gamma (n,3,i)$$ of $$3$$ -subsets of a set of size $$n$$ with adjacency defined by subsets meeting in $$i$$ elements of $$\Omega $$ , where $$0 \le i \le 2$$ . Most of the main parameters are obtained; the hulls, the duals, and other subcodes of the $$C_3(A_i+I)$$ are also examined. [ABSTRACT FROM AUTHOR]

Ternary complexes between the macrocyclic host cucurbit[8]uril, dicationic dyes, and chiral aromatic analytes afford strong induced circular dichroism (ICD) signals in the near-UV and visible regions. This allows for chirality sensing and peptide-sequence recognition in water at low micromolar analyte concentrations. The reversible and noncovalent mode of binding ensures an immediate response to concentration changes, which allows the real-time monitoring of chemical reactions. The introduced supramolecular method is likely to find applications in bioanalytical chemistry, especially enzyme assays, for drug-related analytical applications, and for continuous monitoring of enantioselective reactions, particularly asymmetric catalysis. [ABSTRACT FROM AUTHOR]

The properties of noble gas systems can be greatly extended by heterogeneous mixtures of elements. The geometrical structures and energies of mixed Ar-Kr-Xe clusters were investigated using ternary Lennard-Jones (TLJ) potential. For the ArKrXe, ArKrXe, and ArKrXe ( n = 0-17) clusters investigated, the results show that only two minimum energy configurations exist, i.e., polytetrahedron and six-fold pancake. The inner core of all these clusters is composed mainly of Ar atoms, and Kr and Xe atoms are distributed on the surface with well mixed pattern for polytetrahedral and segregate pattern for six-fold pancake configurations. The relative stability property of Ar-Kr-Xe clusters with a certain composition is discussed. Moreover, the role of heterogeneity on the strain was investigated, and reduced strain energies in Ar-Kr-Xe clusters were studied to find possible ways of reducing strain. The results showed that the strain energies were affected mainly by Ar-Ar, Ar-Kr, and Xe-Xe bonds. [Figure not available: see fulltext.] [ABSTRACT FROM AUTHOR]

Summary: Eukaryotic translation initiation begins with assembly of a 43S preinitiation complex. First, methionylated initiator methionine transfer RNA (Met-tRNAi Met), eukaryotic initiation factor (eIF) 2, and guanosine triphosphate form a ternary complex (TC). The TC, eIF3, eIF1, and eIF1A cooperatively bind to the 40S subunit, yielding the 43S preinitiation complex, which is ready to attach to messenger RNA (mRNA) and start scanning to the initiation codon. Scanning on structured mRNAs additionally requires DHX29, a DExH-box protein that also binds directly to the 40S subunit. Here, we present a cryo-electron microscopy structure of the mammalian DHX29-bound 43S complex at 11.6 Å resolution. It reveals that eIF2 interacts with the 40S subunit via its α subunit and supports Met-tRNAi Met in an unexpected P/I orientation (eP/I). The structural core of eIF3 resides on the back of the 40S subunit, establishing two principal points of contact, whereas DHX29 binds around helix 16. The structure provides insights into eukaryote-specific aspects of translation, including the mechanism of action of DHX29. [ABSTRACT FROM AUTHOR]

Since it is known that interference with each sonar sensor could be effectively reduced when waveforms are appropriately designed for a Sonar Sensor Network (SSN), we provide a set of new ternary codes called optimized punctured Zero Correlation Zone sequence-pair set (ZCZPS) and provide a method to construct such codes. We study the codes' properties especially using the ambiguity function to analyze the nature of the output of the matched filter. We apply our provided ternary codes to the SSN as pulse compression codes for narrowband pulse signals and simulate the target detection performance of the system. Comparing with the classical periodic Gold sequences, our codes could improve the system detection performance. [ABSTRACT FROM AUTHOR]

Abstract: The enumeration of strongly regular graphs with parameters (45, 12, 3, 3) has been completed, and it is known that there are 78 non-isomorphic strongly regular (45, 12, 3, 3) graphs. A strongly regular graph with these parameters is a symmetric (45, 12, 3) design having a polarity with no absolute points. In this paper we examine the ternary codes obtained from the adjacency (resp. incidence) matrices of these graphs (resp. designs), and those of their corresponding derived and residual designs. Further, we give a generalization of a result of Harada and Tonchev on the construction of non-binary self-orthogonal codes from orbit matrices of block designs under an action of a fixed-point-free automorphism of prime order. Using the generalized result we present a complete classification of self-orthogonal ternary codes of lengths 12, 13, 14, and 15, obtained from non-fixed parts of orbit matrices of symmetric (45, 12, 3) designs admitting an automorphism of order 3. Several of the codes obtained are optimal or near optimal for the given length and dimension. We show in addition that the dual codes of the strongly regular (45, 12, 3, 3) graphs admit majority logic decoding. [Copyright &y& Elsevier]

In this paper, we construct two ternary linear codes C(SO(3, q)) and C(O(3, q)), respectively associated with the orthogonal groups SO(3, q) and O(3, q). Here q is a power of three. Then we obtain two recursive formulas for the power moments of Kloosterman sums with "trace nonzero square arguments" in terms of the frequencies of weights in the codes. This is done via Pless power moment identity and by utilizing the explicit expressions of Gauss sums for the orthogonal groups. [ABSTRACT FROM AUTHOR]

Constant-weight codes (CWCs) play an important role in coding theory. The problem of determining the sizes for optimal ternary CWCs with length n, weight 4, and minimum Hamming distance 5 ((n,5,4)3 code) has been settled for all positive integers n\leq 10 or n > 10 and n\equiv 1\pmod 3 with n\in \13,52,58\ undetermined. In this paper, we investigate the problem of constructing optimal (n,5,4)3 codes for all lengths n with the tool of group divisible codes. We determine the size of an optimal (n,5,4)3 code for each integer n\geq 4 leaving the lengths n\in \12,13,21,27,33,39,45,52\ unsolved. [ABSTRACT FROM PUBLISHER]

Constant-composition codes (CCCs) are a generalization of constant weight codes and permutation codes. The concept of group divisible codes, an analog of group divisible designs in combinatorial design theory, was first introduced by Chee et al. This new class of codes has been shown to be useful in recursive constructions of constant-weight codes and constant-composition codes. In this paper, we consider the problem of determining the maximal sizes of ternary constant-composition codes of weight four and distance five using group divisible codes as the main tools. We determine the exact values for these parameters. The previously known results are those with code length no greater than 10. [ABSTRACT FROM AUTHOR]

Recently, Chee and Ling ("Constructions for q-ary constant-weight codes", IEEE Trans. Inf. Theory, vol. 53, no. 1, 135-146, Jan. 2007 ) introduced a new combinatorial construction for q-ary constant-weight codes which reveals a close connection between q-ary constant-weight codes and sets of pairwise disjoint combinatorial designs. In this paper, we study the problem of constructing optimal ternary constant-weight codes with Hamming weight four and minimum distance six using this approach. The construction here exploits completely reducible super simple designs and group divisible codes. The problem is solved leaving only two cases undetermined. Previously, the sizes of constant-weight codes of weight four and distance six were known only for those of length no greater than 10. [ABSTRACT FROM AUTHOR]

Abstract: For a set of size and the set of subsets of of size , we examine the ternary codes obtained from the adjacency matrix of each of the three graphs with vertex set , with adjacency defined by two vertices as -sets being adjacent if they have zero, one or two elements in common, respectively. [Copyright &y& Elsevier]

Abstract: In this note, we consider a construction for optimal ternary constant weight codes (CWCs) via Bhaskar Rao designs (BRDs). The known existence results for BRDs are employed to generate many new optimal nonlinear ternary CWCs with constant weight 4 and minimum Hamming distance 5. [Copyright &y& Elsevier]

We give a simple construction of distance-preserving mappings from ternary vectors to permutations (3-DPM). Our result gives a lower bound for permutation arrays, i.e., P(n, d) ≥ A3(n, d), which significantly improves previous lower bounds for d ≤ .... [ABSTRACT FROM AUTHOR]

We construct a class of vertex operator algebras based on the tricritical 3-state Potts model L(6/7, 0) and some ternary codes. We also compute their irreducible modules. In addition, we show that there is a natural VOA automorphism of order 3 or 1 associated with a subalgebra isomorphic to L(6/7, 0) ⊕ L(6/7, 5). [ABSTRACT FROM AUTHOR]

In this paper we study the bivariate theta-series which can be attached to the complete weight enumerator of ternary codes. We give an injective homorphism between the ring of invariants of a certain matrix group and the ring of Jacobi modular forms. This generalizes to Jacobi forms a result of Broue´ and Enguehard [Ann. Sci. E´cole Norm. Sup. 5 (4) (1972) 157–181] on classical modular forms. [Copyright &y& Elsevier]

One of the most important problems of coding theory is to construct codes with best possible minimum distances. Recently, quasi-cyclic (QC) codes have been proven to contain many such codes. In this paper, we consider quasi-twisted (QT) codes, which are generalizations of QC codes, and their structural properties and obtain new codes which improve minimum distances of best known linear codes over the finite fields GF(3) and GF(5). Moreover, we give a BCH-type bound on minimum distance for QT codes and give a sufficient condition for a QT code to be equivalent to a QC code. [ABSTRACT FROM AUTHOR]

The weight hierarchy of a linear [n,k;q] code C over GF(q) is the sequence (d/sub 1/,d/sub 2/,...d/sub k/) where d/sub /spl tau// is the smallest support of an /spl tau/-dimensional subcode of C. The possible weight hierarchies of [n,4;q] codes are studied. In particular, the possible weight hierarchies of [n,4;3] codes are determined. [ABSTRACT FROM PUBLISHER]

The covering radius of all ternary cyclic codes of length up to 25 is given. Some of the results were obtained by computer and for others mathematical reasonings were applied. The minimal distances of all codes were recalculated. [ABSTRACT FROM AUTHOR]

Let d3(n,k) be the maximum possible minimum Hamming distance of a ternary [ n,k,d;3]-code for given values of n and k. It is proved that d3(44,6)=27, d3(76,6)=48,d3(94,6)=60 , d3(124,6)=81,d3(130,6)=84 , d3(134,6)=87,d3(138,6)=90 , d3(148,6)=96,d3(152,6)=99 , d3(156,6)=102,d3(164,6)=108 , d3(170,6)=111,d3(179,6)=117 , d3(188,6)=123,d3(206,6)=135 , d3(211,6)=138,d3(224,6)=147 , d3(228,6)=150,d3(236,6)=156 , d3(31,7)=17 and d3(33,7)=18 . These results are obtained by a descent method for designing good linear codes. [ABSTRACT FROM AUTHOR]