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Two skew Hadamard matrices are considered {\sf SH}-equivalent if they are similar by a signed permutation matrix. This paper determines the number of {\sf SH}-inequivalent skew Hadamard matrices of order $36$ for some types. We also study ternary sel
Externí odkaz:
http://arxiv.org/abs/2402.11074
A classification of Hadamard matrices of order $2p+2$ with an automorphism of order $p$ is given for $p=29$ and $31$. The ternary self-dual codes spanned by the newly found Hadamard matrices of order $60$ with an automorphism of order $29$ are comput
Externí odkaz:
http://arxiv.org/abs/2307.08983
Autor:
Araya, Makoto, Harada, Masaaki
We give restrictions on the weight enumerators of ternary near-extremal self-dual codes of length divisible by $12$ and quaternary near-extremal Hermitian self-dual codes of length divisible by $6$. We consider the weight enumerators for which there
Externí odkaz:
http://arxiv.org/abs/2212.01080
In 2013, Nebe and Villar gave a series of ternary self-dual codes of length $2(p+1)$ for a prime $p$ congruent to $5$ modulo $8$. As a consequence, the third ternary extremal self-dual code of length $60$ was found. We show that the ternary self-dual
Externí odkaz:
http://arxiv.org/abs/2205.15498
Autor:
Araya, Makoto, Harada, Masaaki
We propose a method for a classification of quaternary Hermitian LCD codes having large minimum weights. As an example, we give a classification of quaternary optimal Hermitian LCD codes of dimension 3.
Externí odkaz:
http://arxiv.org/abs/2011.04139
Linear complementary dual (LCD) codes are linear codes that intersect with their dual codes trivially. We study the largest minimum weight $d_2(n,k)$ among all binary LCD $[n,k]$ codes and the largest minimum weight $d_3(n,k)$ among all ternary LCD $
Externí odkaz:
http://arxiv.org/abs/1908.08661
Linear complementary dual (LCD) codes are linear codes that intersect with their dual trivially. We give a characterization of LCD codes over $\mathbb{F}_q$ having large minimum weights for $q \in \{2,3\}$. Using the characterization, we determine th
Externí odkaz:
http://arxiv.org/abs/1908.03294
Publikováno v:
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 66, 2020 2751-2759
The largest minimum weights among quaternary Hermitian linear complementary dual codes are known for dimension $2$. In this paper, we give some conditions for the nonexistence of quaternary Hermitian linear complementary dual codes with large minimum
Externí odkaz:
http://arxiv.org/abs/1904.07517
Akademický článek
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Autor:
Araya, Makoto, Harada, Masaaki
Publikováno v:
Cryptography and Communications (2020) 12:285-300
Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. We study the largest minimum weight $d(n,k)$ among all binary linear complementary dual $[n,k]$ codes. We determine $
Externí odkaz:
http://arxiv.org/abs/1807.03525