具有小尺寸外壳的MDS多扭曲里德-所罗门码

Cryptography and Communications Pub Date : 2023-12-04 DOI:10.1007/s12095-023-00688-6

Harshdeep Singh, Kapish Chand Meena

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引用次数: 3

摘要

本文给出了多扭曲Reed-Solomon码是MDS的一个充分必要条件。特别地，我们引入了一类新的MDS双扭曲Reed-Solomon码\(\mathcal {C}_{\varvec{\alpha , t, h, \eta }}\)，它在有限域\(\mathbb {F}_q\)上扭曲\(\varvec{t} = (1, 2)\)和钩子\(\varvec{h} = (0, 1)\)，提供了一个在\(\mathbb {F}_{16}\)上的非平凡示例和在大小不超过17的有限域上的枚举。此外，我们还得到了具有小维壳体的多捻Reed-Solomon码存在的必要条件。由此，我们得到了具有小维壳体的MDS多扭曲Reed-Solomon码存在的条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

MDS multi-twisted Reed-Solomon codes with small dimensional hull

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MDS multi-twisted Reed-Solomon codes with small dimensional hull

In this paper, we find a necessary and sufficient condition for multi-twisted Reed-Solomon codes to be MDS. In particular, we introduce a new class of MDS double-twisted Reed-Solomon codes \(\mathcal {C}_{\varvec{\alpha , t, h, \eta }}\) with twists \(\varvec{t} = (1, 2)\) and hooks \(\varvec{h} = (0, 1)\) over the finite field \(\mathbb {F}_q\), providing a non-trivial example over \(\mathbb {F}_{16}\) and enumeration over the finite fields of size up to 17. Moreover, we obtain necessary conditions for the existence of multi-twisted Reed-Solomon codes with small dimensional hull. Consequently, we derive conditions for the existence of MDS multi-twisted Reed-Solomon codes with small dimensional hull.

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Cryptography and Communications

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