Results 41 to 50 of about 9,454,079 (375)
Code algebras, axial algebras and VOAs [PDF]
, 2018 Inspired by code vertex operator algebras (VOAs) and their representation theory, we define code algebras, a new class of commutative non-associative algebras constructed from binary linear codes. Let $C$ be a binary linear code of length $n$.
Castillo-Ramirez, Alonso +2 more
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Maximum Intersection of Linear Codes and Codes Equivalent to Linear
Journal of Applied and Industrial Mathematics, 2019 Summary: We consider linear codes in a space over a finite field with the Hamming metric. A code is called pseudolinear if it is the image of a linear code under an isometric transformation of the space. We derive an upper bound \((q-2)M/q\) attainable for \(q\geqslant 3\) for the size of the intersection of two different pseudolinear codes of the same
Avgustinovich, Sergeĭ Vladimirovich +1 more
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Coupling JOREK and STARWALL for Non-linear Resistive-wall Simulations [PDF]
, 2012 The implementation of a resistive-wall extension to the non-linear MHD-code JOREK via a coupling to the vacuum-field code STARWALL is presented along with first applications and benchmark results.
Chu M S +16 more
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On Weight Spectrum of Linear Codes [PDF]
2021 XVII International Symposium "Problems of Redundancy in Information and Control Systems" (REDUNDANCY), 2021 We study sequences of linear or affine codes with uniform weight spectrum, i.e., a part of codewords with any fixed weight tends to zero. It is proved that a sequence of linear codes has a uniform weight spectrum if the number of vectors from codes with weight $1$ grows to infinity.
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On the generalized Hamming weights of certain Reed–Muller-type codes
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020 There is a nice combinatorial formula of P. Beelen and M. Datta for the r-th generalized Hamming weight of an a ne cartesian code. Using this combinatorial formula we give an easy to evaluate formula to compute the r-th generalized Hamming weight for a ...
González-Sarabia Manuel +2 more
doaj +1 more source
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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From Skew-Cyclic Codes to Asymmetric Quantum Codes [PDF]
, 2010 We introduce an additive but not $\mathbb{F}_4$-linear map $S$ from $\mathbb{F}_4^{n}$ to $\mathbb{F}_4^{2n}$ and exhibit some of its interesting structural properties.
A. R. Calderbank +16 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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Low Complexity Encoding for Network Codes [PDF]
, 2006 In this paper we consider the per-node run-time complexity of network multicast codes. We show that the randomized algebraic network code design algorithms described extensively in the literature result in codes that on average require a number of ...
Cassuto, Yuval +2 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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