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Frameproof codes (FPCs) are widely studied as they are classic fingerprinting codes that can protect copyrighted materials. The main interests are construction methods and bounds of the number of codewords of FPCs for a fixed length when the alphabet size approaches infinity. In this paper, we focus on the upper bound of the size of FPCs when the fixed length is 4 and the strength is 2. We obtain an upper bound 2q2-2q+7 on the size of a q-ary 2-FPC of length 4 for any positive integer q>48. The best previously well known bound of this type of FPCs is 2q2-2, which is due to Blackburn (SIAM J Discret Math 16:499-510, 2003). Our new upper bound improves the previous upper bound and it is not very far from the current best lower bound 2q2-4q+3 obtained from the explicit construction due to Chee and Zhang (IEEE Trans Inf Theory 58:5449-5453, 2012). [ABSTRACT FROM AUTHOR]

The binary-coded decimal (BCD) being the more accurate and human-readable representation with ease of conversion is prevailing in the computing and electronic communication. In this paper, a tree-structured parallel BCD addition algorithm is proposed with the reduced time complexity O(N(log2b)+(N-1)), where N = number of digits and b = number of bits in a digit. BCD adder is more effective with a lookup table (LUT)-based design, due to field programmable gate array (FPGA) technology’s enumerable benefits and applications. A size-minimal and depth-minimal LUT-based BCD adder circuit construction is the main contribution of this paper. The proposed parallel BCD adder gains a radical achievement compared to the existing best known LUT-based BCD adders. The proposed BCD adder is coded in VHDL and implemented in a Virtex-6 platform targeting XC6VLX75T Xilinx FPGA with a -3 speed grade by using ISE 13.1. The proposed BCD adder provides prominent better performance with 20.0% reduction in area and 41.32% reduction in delay for the post-layout simulation. Since the proposed circuit is improved in both area and delay parameter, it is 53.06% efficient in terms of area-delay product compared to the best known existing BCD adder, which is surely a significant achievement. Moreover, the proposed design consumes 34.28% less power in comparison with existing best known approach at a clock frequency of 200 MHz and a reference voltage of 5 V. [ABSTRACT FROM AUTHOR]

Traditional projection environments typically comprise projectors and custom-built projection screens in a static setting. However, with the availability of embedded and standalone pico-projectors, the representative use-case of such hand-held projectors is shifting from static to mobile. Users are increasingly using such devices to project content in random indoor environments that are cluttered and hence not completely suitable for projection. This paper proposes a robust binary-coded pattern that enables the reliable selection of a clutter-free sub-surface from within the projected area and thus allows the confinement of projection to the selected sub-region. Experiments confirm that the proposed pattern provides better resilience to the detection errors as compared to the state-of-the-art binary-coded patterns for the case of mobile-grade low-resolution pico-projectors. [ABSTRACT FROM AUTHOR]

Reversible logic, as an interesting and important issue, has been widely used in designing combinational and sequential circuits for low-power and high-speed computation. Though a significant number of works have been done on reversible combinational logic, the realization of reversible sequential circuit is still at premature stage. Reversible counter is not only an important part of the sequential circuit but also an essential part of the quantum circuit system. In this paper, we designed two kinds of novel reversible counters. In order to construct counter, the innovative reversible T Flip-flop Gate (TFG), T Flip-flop block (T_FF) and JK flip-flop block (JK_FF) are proposed. Based on the above blocks and some existing reversible gates, the 4-bit binary-coded decimal (BCD) counter and controlled Up/Down synchronous counter are designed. With the help of Verilog hardware description language (Verilog HDL), these counters above have been modeled and confirmed. According to the simulation results, our circuits' logic structures are validated. Compared to the existing ones in terms of quantum cost (QC), delay (DL) and garbage outputs (GBO), it can be concluded that our designs perform better than the others. There is no doubt that they can be used as a kind of important storage components to be applied in future low-power computing systems. [ABSTRACT FROM AUTHOR]

Partial product generation (PPG), in radix-10 multiplication hardware, is often done through selection of pre-computed decimal multiples of the multiplicand. However, ASIC and FPGA realization of classical PPG via digit-by-digit multiplication has recently attracted some researchers. For example, a sequential multiplier, squarer, divider, FPGA parallel multiplier, and array multiplier are all based on a specific binary-coded decimal (BCD) digit multiplier (BDM). Most BDMs, as we have encountered, compute the binary product of two 1-digit BCD operands, and convert it to 2-digit BCD product. We provide our own version of two of these works with some adjustments and improvements, and offer two new low-cost BDMs in this category. However, a recent FPGA BDM uses straightforward truth table approach from scratch and skips binary product generation. We redesign the latter via low-level FPGA programming, and also provide its ASIC realization. We synthesize all the studied and new designs on ASIC and FPGA platforms, exhaustively check them for correctness, and compare their performance, to show that our two new designs, and the ASIC and new FPGA realizations of the aforementioned fully truth table-based design, outperform the previous ones in terms of one or more figures of merit. [ABSTRACT FROM AUTHOR]

In this paper we study the construction and the enumeration of binary words in $$\{0,1\}^*$$ having more 1's than 0's and avoiding a set of cross-bifix-free patterns. We give a particular succession rule, called jumping and marked succession rule, which describes the growth of such words according to their number of ones. Moreover, the problem of associating a word to a path in the generating tree obtained by the succession rule is solved by introducing an algorithm which constructs all binary words having more 1's than 0's and then kills those containing the forbidden patterns. Finally, we give the generating function of such words according to the number of ones. [ABSTRACT FROM AUTHOR]

We prove that arbitrary n-ary quasigroups of order 4 can be transformed into each other by successive switchings of {a, b}-components. We prove that perfect (closely packed) binary codes with distance 3 whose rank (dimension of the linear span) is greater by 1 or 2 than the rank of a linear perfect code can be taken to each other by successive switchings of i-components. [ABSTRACT FROM AUTHOR]

We show that subclasses of q-ary separable Goppa codes Γ( L, G) with L = {α ∈ GF( q): G(α) ∈ 0} and with special Goppa polynomials G( x) can be represented as a chain of equivalent and embedded codes. For all codes of the chain we obtain an improved bound for the dimension and find an exact value of the minimum distance. A chain of binary codes is considered as a particular case with specific properties. [ABSTRACT FROM AUTHOR]

Inaccuracies in computations in the paper of the authors on classification of perfect binary codes of lengths 15 and 16 and of rank 13 are fixed. An explicit construction of all extended perfect codes of length 16 and rank 13 with a given kernel size is presented. Perfect binary codes of length 15 and rank 14 obtained by the general doubling construction are classified. [ABSTRACT FROM AUTHOR]

Let K = (k1, k2, …, kr) and L = (l1, l2, …, ls) be sets of nonnegative integers. Let F = (F1, F2, …, Fm) be a family of subsets of [n] with [Fi] ϵ K for each i and ∣Fi ∩ Fj∣ ϵ L for any i≠j. Every subset Fe of [n] can be represented by a binary code a = (a1, a2, …, an) such that ai = 1 if i ϵ Fe and ai = 0 if iϵFe. Alon et al. made a conjecture in 1991 in modular version. We prove Alon-Babai-Sukuki's Conjecture in nonmodular version. For any K and L with n ⩾ s + max ki, ∣F∣ ⩽ (n-1 s ) + (n-1 s-1) + … + (n-1 s-2r+1). [ABSTRACT FROM AUTHOR]

A method of control is proposed on the basis of representing the checked circuits as consequently connected subcircuits (cascades). The subdivision of the circuits into cascades is made in such a way that any failure in each of them results in a distortion of no more than one binary digit at its input. There is developed an universal sequential-sampling circuit with step-by-step control, where the detection of errors does not require additional (coding) variables. The results of this investigation showed that the proposed method for operational control entails considerably lesser hardware and power expenditure as compared with the circuits based on application of the Berger code. [ABSTRACT FROM AUTHOR]

This work presents a brief survey on codes (with respect to Hamming metric) which are perfect-like i.e. codes which are capable to correct a given set of error vectors and no others. Several kinds of such codes which exist in the literature have been discussed and possibilities of the existence of such codes in some cases have been explored. [ABSTRACT FROM AUTHOR]

We recover the first linear programming bound of McEliece, Rodemich, Rumsey, and Welch for binary error-correcting codes and designs via a covering argument. It is possible to show, interpreting the following notions appropriately, that if a code has a large distance, then its dual has a small covering radius and, therefore, is large. This implies the original code to be small. We also point out that this bound is a natural isoperimetric constant of the Hamming cube, related to its Faber–Krahn minima. While our approach belongs to the general framework of Delsarte’s linear programming method, its main technical ingredient is Fourier duality for the Hamming cube. In particular, we do not deal directly with Delsarte’s linear program or orthogonal polynomial theory. [ABSTRACT FROM AUTHOR]

Abstract  We investigate further the new approach towards the classification of periodic binary sequences into nonlinear complexity classes that commenced in the paper by Petrides and Mykkeltveit (Proceedings of SETA’06 international conference on sequences and their applications, 2006). Nonlinear complexity was first introduced by Jansen (Investigations on nonlinear streamcipher systems: construction and evaluation methods, PhD thesis, 1989) and several attempts have since been made to make it of more practical cryptographic interest. In this direction, we will follow with this article. In particular we perform composition of the recursions found in the (2006) article which are related to nonlinear complexity, and prove some of its missing results. Studying the properties of the composition operation for a certain type of recursions is an alternative to study all possible recursions, as required for completing the above mentioned classification. A complete classification will allow, amongst other things, construction of statistical tests to assess the cryptographic strength of binary sequences used in stream ciphers. [ABSTRACT FROM AUTHOR]

Abstract  By counting the coset leaders for cosets of weight 3 of the Melas code we give a new proof for the characterization of Kloosterman sums divisible by 3 for $${\mathbb{F}_{2^m}}$$ where m is odd. New results due to Charpin, Helleseth and Zinoviev then provide a connection to a characterization of all $${a\in\mathbb{F}_{2^m}}$$ such that $${Tr(a^{1/3})=0}$$; we prove a generalization to the case $${Tr(a^{1/(2^k-1)})=0}$$. We present an application to constructing caps in PG(n, 2) with many free pairs of points. [ABSTRACT FROM AUTHOR]

Fingerprinting provides a means of tracing unauthorized redistribution of digital data by individually marking each authorized copy with a personalized serial number. In order to prevent a group of users from collectively escaping identification, collusion-secure fingerprinting codes have been proposed. In this paper, we introduce a new construction of a collusion-secure fingerprinting code which is similar to a recent construction by Tardos but achieves shorter code lengths and allows for codes over arbitrary alphabets. We present results for ‘symmetric’ coalition strategies. For binary alphabets and a false accusation probability $$\varepsilon_1$$ , a code length of $$m\approx \pi^2 c_0^2\ln\frac{1}{\varepsilon_1}$$ symbols is provably sufficient, for large c 0, to withstand collusion attacks of up to c 0 colluders. This improves Tardos’ construction by a factor of 10. Furthermore, invoking the Central Limit Theorem in the case of sufficiently large c 0, we show that even a code length of $$m\approx 1/2\pi^2 c_0^2\ln\frac{1}{\varepsilon_1}$$ is adequate. Assuming the restricted digit model, the code length can be further reduced by moving from a binary alphabet to a q-ary alphabet. Numerical results show that a reduction of 35% is achievable for q = 3 and 80% for q = 10. [ABSTRACT FROM AUTHOR]

The covering radius of binary 2-surjective codes of maximum length is studied in the paper. It is shown that any binary 2-surjective code of M codewords and of length $$n = {M-1 \choose \left\lfloor(M-2)/2\right\rfloor}$$ has covering radius $$\frac{n}{2} - 1$$ if M - 1 is a power of 2, otherwise $$\left\lfloor\frac{n}{2}\right\rfloor$$ . Two different combinatorial proofs of this assertion were found by the author. The first proof, which is written in the paper, is based on an existence theorem for k-uniform hypergraphs where the degrees of its vertices are limited by a given upper bound. The second proof, which is omitted for the sake of conciseness, is based on Baranyai’s theorem on l-factorization of a complete k-uniform hypergraph. [ABSTRACT FROM AUTHOR]

We show that the linear complexity of a u2 v -periodic binary sequence, u odd, can easily be calculated from the linear complexities of certain 2 v -periodic binary sequences. Since the linear complexity of a 2 v -periodic binary sequence can efficiently be calculated with the Games-Chan algorithm, this leads to attractive procedures for the determination of the linear complexity of a u2 v -periodic binary sequence. Realizations are presented for u  = 3, 5, 7, 15. [ABSTRACT FROM AUTHOR]

Local binary patterns (LBPs) are one of the features which have been used for texture classification. In this paper, a method based on using these features is proposed for fabric defect detection. In the training stage, at first step, LBP operator is applied to an image of defect free fabric, pixel by pixel, and the reference feature vector is computed. Then this image is divided into windows and LBP operator is applied to each of these windows. Based on comparison with the reference feature vector, a suitable threshold for defect free windows is found. In the detection stage, a test image is divided into windows and using the threshold, defective windows can be detected. The proposed method is multiresolution and gray scale invariant and can be used for defect detection in patterned and unpatterned fabrics. Because of its simplicity, online implementation is possible as well. [ABSTRACT FROM AUTHOR]

Starting from a succession rule for Catalan numbers, we define a procedure for encoding and listing the objects enumerated by these numbers such that two consecutive codes of the list differ only by one digit. The Gray code we obtain can be generalized to all the succession rules with the stability property: each label ( k) has in its productions two labels c 1 and c 2, always in the same position, regardless of k. Because of this link, we define Gray structures as the sets of those combinatorial objects whose construction can be encoded by a succession rule with the stability property. This property is a characteristic that can be found among various succession rules, such as the finite, factorial or transcendental ones. We also indicate an algorithm which is a very slight modification of Walsh’s one, working in O(1) worst-case time per word for generating Gray codes. [ABSTRACT FROM AUTHOR]

The effect of plasma microfields on Coulomb collisions between the particles is considered. It is shown that perturbations from other particles insignificantly affect the frequency of short-range collisions. The results of calculating the pair correlation function of the particles in a plasma for distances much shorter than the interparticle distance agree well with predictions of the binary theory. [ABSTRACT FROM AUTHOR]

Abstract  A pointed variety of universal algebras is protomodular in the sense of D. Bourn, if and only if it is classically ideal determined in the sense of A. Ursini (this result is due to D. Bourn and G. Janelidze). We prove a characterization theorem for pointed protomodular categories, which is a (pointed) categorical version of Ursini’s characterization theorem for classically ideal determined varieties, involving classically 0-regular algebras. A suitable simplification of the property of a pair of relations, which is used to define a classically 0-regular algebra, yields a new closedness property of a single binary relation – we show that a finitely complete pointed category is protomodular if and only if every binary internal relation R→A 2 in it has this closedness property. [ABSTRACT FROM AUTHOR]