On equidistant single-orbit cyclic and quasi-cyclic subspace codes

IF 1.4 2区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Designs, Codes and Cryptography Pub Date : 2025-02-12 DOI:10.1007/s10623-025-01586-z

Mahak, Maheshanand Bhaintwal

引用次数: 0

Abstract

A code is said to be equidistant if the distance between any two distinct codewords of the code is the same. In this paper, we have studied equidistant single-orbit cyclic and quasi-cyclic subspace codes. The orbit code generated by a subspace U in \({\mathbb {F}}_{q^n}\) such that the dimension of U over \({\mathbb {F}}_q\) is t or \(n-t\), \(\text{ where }~t=\dim _{{\mathbb {F}}_q}(\text{ Stab }(U)\cup \{0\})\), is equidistant and is termed a trivial equidistant orbit code. Using the concept of cyclic difference sets, we have proved that only the trivial equidistant single-orbit cyclic subspace codes exist. Further, we have explored equidistant single-orbit quasi-cyclic subspace codes, focusing specifically on those which are sunflowers.

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关于等距单轨循环和拟循环子空间码

如果码的任意两个不同码字之间的距离相同，则称码是等距的。本文研究了等距单轨循环和拟循环子空间码。由\({\mathbb {F}}_{q^n}\)中的子空间U生成的轨道码使得U在\({\mathbb {F}}_q\)上的维数为t或\(n-t\), \(\text{ where }~t=\dim _{{\mathbb {F}}_q}(\text{ Stab }(U)\cup \{0\})\)是等距的，称为平凡等距轨道码。利用循环差分集的概念，证明了只有平凡等距单轨循环子空间码存在。此外，我们还探讨了等距单轨准循环子空间码，特别关注那些向日葵。

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

Designs, Codes and Cryptography 工程技术-计算机：理论方法

CiteScore

2.80

自引率

12.50%

发文量

157

审稿时长

16.5 months

期刊介绍： Designs, Codes and Cryptography is an archival peer-reviewed technical journal publishing original research papers in the designated areas. There is a great deal of activity in design theory, coding theory and cryptography, including a substantial amount of research which brings together more than one of the subjects. While many journals exist for each of the individual areas, few encourage the interaction of the disciplines. The journal was founded to meet the needs of mathematicians, engineers and computer scientists working in these areas, whose interests extend beyond the bounds of any one of the individual disciplines. The journal provides a forum for high quality research in its three areas, with papers touching more than one of the areas especially welcome. The journal also considers high quality submissions in the closely related areas of finite fields and finite geometries, which provide important tools for both the construction and the actual application of designs, codes and cryptographic systems. In particular, it includes (mostly theoretical) papers on computational aspects of finite fields. It also considers topics in sequence design, which frequently admit equivalent formulations in the journal’s main areas. Designs, Codes and Cryptography is mathematically oriented, emphasizing the algebraic and geometric aspects of the areas it covers. The journal considers high quality papers of both a theoretical and a practical nature, provided they contain a substantial amount of mathematics.