Results 21 to 30 of about 216,076 (266)
Linear codes resulting from finite group actions [PDF]
Transactions on Combinatorics, 2022 In this article, we use group action theory to define some important ternary linear codes. Some of these codes are self-orthogonal having a minimum distance achieving the lower bound in the previous records. Then, we define two new codes sharing the same
Driss Harzalla
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On the Trifference Problem for Linear Codes
IEEE Transactions on Information Theory, 2022 We prove that perfect $3$-hash linear codes in $\mathbb{F}_{3}^{n}$ must have dimension at most $ \left(\frac{1}{4}-ε\right)n$ for some absolute constant $ε> 0$.
Cosmin Pohoata, Dmitriy Zakharov
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Моделирование и анализ информационных систем, 2022 Line codes are widely used to protect against errors in data transmission and storage systems, to ensure the stability of various cryptographic algorithms and protocols, to protect hidden information from errors in a stegocontainer. One of the classes of
Yury V. Kosolapov +2 more
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On Linear Complementary Pairs of Codes [PDF]
IEEE Transactions on Information Theory, 2018 We study linear complementary pairs (LCP) of codes $(C, D)$ , where both codes belong to the same algebraic code family. We especially investigate constacyclic and quasi-cyclic LCP of codes. We obtain characterizations for LCP of constacyclic codes and LCP of quasi-cyclic codes.
Claude Carlet +4 more
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Design of Non-Adaptive Querying Policies Based on Error Control Coding
IEEE Access, 2020 This paper designs non-adaptive querying policies (NQPs) for the noisy 20 questions game based on error-correction codes. The querying accuracy of a specific NQP is upper bounded by a function of the minimum distance among its codewords. As a result, the
Shuai Wang +3 more
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Quasi-linear network coding [PDF]
2014 International Symposium on Network Coding (NetCod), 2014 We present a heuristic for designing vector non-linear network codes for non-multicast networks, which we call quasi-linear network codes. The method presented has two phases: finding an approximate linear network code over the reals, and then quantizing it to a vector non-linear network code using a fixed-point representation.
Moshe Schwartz 0001, Muriel Médard
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Optimal Linear Codes and Their Hulls
MathematicsThe hull of a linear code C is the intersection of C with its dual code. The goal is to study the dimensions of the hulls of optimal binary and ternary linear codes for a given length and dimension.
Stefka Bouyuklieva +1 more
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On the Covering Dimension of a Linear Code [PDF]
IEEE Transactions on Information Theory, 2016 The critical exponent of a matroid is one of the important parameters in matroid theory and is related to the Rota and Crapo's Critical Problem. This paper introduces the covering dimension of a linear code over a finite field, which is analogous to the critical exponent of a representable matroid.
Britz, T, Shiromoto, K
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Linear Codes and Self-Polarity
MathematicsThis work studies projective self-dual (PSD) and self-polar linear codes over finite fields with q elements, where q is a power of a prime. The possible parameters for which PSD codes may exist are presented, and many examples are provided.
Iliya Bouyukliev +3 more
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Discrete Mathematics, 1985 Several new and interesting properties of 'linear intersecting codes' are studied. The cyclic structure as well as the duals of such codes are also discussed. Relationships of such codes with many well-known codes in the binary and non-binary cases are established. Almost every study made in the paper is illustrated with an interesting example.
Gérard D. Cohen, Abraham Lempel
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