Generalized Singleton Type Upper Bounds

被引：2

作者：

Chen, Hao ^{[1
]}

Qu, Longjiang ^{[2
]}

Li, Chengju ^{[3
]}

Lyu, Shanxiang ^{[1
]}

Xu, Liqing ^{[1
]}

Zhou, Mingshuo ^{[4
]}

机构：

[1] Jinan Univ, Coll Informat Sci & Technol Cyber Secur, Guangzhou 510632, Guangdong, Peoples R China

[2] Natl Univ Def Technol, Coll Liberal Arts & Sci, Changsha 410073, Hunan, Peoples R China

[3] East China Normal Univ, Shanghai Key Lab Trustworthy Comp, Shanghai 200062, Peoples R China

[4] Tianjin Univ, Ctr Appl Math, Sch Math, Tianjin, Peoples R China

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2024年 / 70卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Covering code; generalized singleton type upper bound; symbol-pair code; insertion-deletion code; singleton-optimal locally recoverable code; BINARY LINEAR CODES; LOCALLY REPAIRABLE CODES; COVERING RADIUS; GEOMETRY; WEIGHTS; NUMBER;

D O I：

10.1109/TIT.2023.3346179

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we give many new Singleton type upper bounds on the sizes of codes with given minimum Hamming distances. These upper bounds are stronger than the Griesmer bound when the lengths of codes are large. Some upper bounds on the lengths of general small Singleton defect codes are presented. Our generalized Singleton type upper bounds have wide applications to symbol-pair codes, insertion-deletion codes and locally recoverable codes. The generalized Singleton type upper bounds on symbol-pair codes and insertion-deletion codes are much stronger than the direct Singleton bounds on symbol-pair codes and insertion-deletion codes when the lengths are large and the Hamming minimum distances are small. Upper bounds on the lengths of small dimension optimal locally recoverable codes and small dimension optimal (r, delta) locally recoverable codes with any given minimum distance are also presented.

引用

页码：3298 / 3308

页数：11

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