Self-dual codes over <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">F</mml:mi></mml:mrow><mml:mrow><mml:mn>5</mml:mn></mml:mrow></mml:msub></mml:math> and s-extremal unimodular lattices

Harada, Masaaki

doi:10.1016/j.disc.2022.113126

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2024

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Cited by 3 publications

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“…For small fields F, many four circulant (negacirculant) self-dual codes over F having large minimum weights are known (see e.g., [7], [13], [14], [15] and the references given therein). In this paper, by modifying four circulant self-dual codes, we give a method for constructing quaternary Hermitian self-dual codes based on μ-circulant matrices, which are called modified four μ-circulant codes.…”

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confidence: 99%

A method for constructing quaternary Hermitian self-dual codes and an application to quantum codes

Harada

2024

Des. Codes Cryptogr.

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We introduce quaternary modified four $$\mu $$ μ -circulant codes as a modification of four circulant codes. We give basic properties of quaternary modified four $$\mu $$ μ -circulant Hermitian self-dual codes. We also construct quaternary modified four $$\mu $$ μ -circulant Hermitian self-dual codes having large minimum weights. Two quaternary Hermitian self-dual [56, 28, 16] codes are constructed for the first time. These codes improve the previously known lower bound on the largest minimum weight among all quaternary (linear) [56, 28] codes. In addition, these codes imply the existence of a quantum [[56, 0, 16]] code.

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