Large cyclic subspace codes over finite fields

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2025-09-08 DOI:10.1016/j.ffa.2025.102722

He Zhang , Chunming Tang , Xiwang Cao , Gaojun Luo

引用次数: 0

Abstract

Cyclic subspace codes play a crucial role in random network coding. Designing such cyclic subspace codes with the largest possible code size and minimum distance remains a classical problem. Roth et al. (2018) [28] first investigated optimal cyclic subspace codes via Sidon spaces and proved that the orbit of a Sidon space is an optimal cyclic subspace code with full-length orbit. This paper introduces a new method, namely the intermediate extension field, to construct Sidon spaces and cyclic subspace codes. The main results show that our new codes over intermediate fields have optimal minimum distance and contain more codewords than known constructions. Therefore, this work improves the lower bound of optimal cyclic subspace codes.

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有限域上的大循环子空间码

循环子空间码在随机网络编码中起着至关重要的作用。设计尽可能大码长和最小距离的循环子空间码仍然是一个经典问题。Roth et al.(2018)[28]首次通过西顿空间研究了最优循环子空间码，证明了西顿空间的轨道是具有全长轨道的最优循环子空间码。本文介绍了构造西顿空间和循环子空间码的一种新方法，即中间可拓域。主要结果表明，我们的新码在中间域上具有最佳的最小距离，并且比已知结构包含更多的码字。因此，本文改进了最优循环子空间码的下界。

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.