Large optimal cyclic subspace codes

被引：6
作者：
Zhang, He [1 ]
Tang, Chunming [1 ,2 ]
Cao, Xiwang [3 ]
机构：
[1] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510006, Peoples R China
[2] Guangzhou Univ, Guangdong Prov Key Lab Informat Secur Technol, Guangzhou 510006, Peoples R China
[3] Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 211100, Peoples R China
来源：
DISCRETE MATHEMATICS | 2024年 / 347卷 / 07期
基金：
中国国家自然科学基金;
关键词：
Constant dimension codes; Optimal minimum distance; Sidon spaces; Cyclic subspace codes; SIDON SPACES; CONSTRUCTION;
D O I：
10.1016/j.disc.2024.114007
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Constant dimension codes, a specialized subclass of subspace codes, have garnered significant attention in recent years due to their applications in random network coding. Among these codes, large cyclic constant dimension codes, endowed with optimal minimum distance, offer efficient solutions for encoding and decoding algorithms. This paper is dedicated to the design of cyclic constant dimension codes that achieve the dual goals: maximizing code size while maintaining optimal minimum distance. We first explore a new form of Sidon spaces and employ this new form to construct several families of cyclic subspace codes. Our codes have optimal minimum distances and have more codewords than previous constructions in the literature. (c) 2024 Elsevier B.V. All rights reserved.
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页数：8
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