Two families of self-orthogonal codes with applications in LCD codes and optimally extendable codes

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2025-05-29 DOI:10.1016/j.ffa.2025.102659

Dengcheng Xie, Shixin Zhu

引用次数: 0

Abstract

Self-orthogonal codes have interesting applications in quantum codes, linear complementary dual (LCD) codes and lattices. LCD codes and (almost) optimally extendable codes are useful to safeguard against Side-Channel Attacks (SCAs) and Fault Injection Attacks (FIAs). In this paper, we first give a lower bound of dual distances for augmented codes via the defining-set construction. Then we construct two families of q-ary self-orthogonal codes with determined weight distributions via defining-set construction and propose the parameters of their duals. Besides, several families of AMDS codes are obtained as byproducts, which are both length-optimal and dimension-optimal with respect to the Sphere-packing bound. As applications, these self-orthogonal codes are used to construct LCD codes and proved to be optimally extendable. As a consequence, our constructions produce some optimal codes.

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两族自正交码及其在LCD码和最优可扩展码中的应用

自正交码在量子码、线性互补对偶码和晶格中有着有趣的应用。LCD代码和（几乎）最佳可扩展代码对于防止侧信道攻击（sca）和故障注入攻击（FIAs）非常有用。本文首先通过定义集构造给出增广码的对偶距离下界。然后，通过定义集构造构造了两类权分布确定的q元自正交码，并给出了它们对偶的参数。此外，作为副产物，我们还得到了一些AMDS码族，它们对于球填充界来说是长度最优的，也是尺寸最优的。作为应用，这些自正交码被用于构造LCD码，并被证明具有最佳的可扩展性。因此，我们的结构产生了一些最优的代码。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Finite Fields and Their Applications 数学-数学

CiteScore

2.00

自引率

20.00%

发文量

133

审稿时长

6-12 weeks

期刊介绍： Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering. For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods. The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.