Bounds in the Lee metric and optimal codes

被引：4

作者：

Byrne, Eimear ^{[1
]}

Weger, Violetta ^{[2
]}

机构：

[1] Univ Coll Dublin, Dublin 4, Dublin D04V1W8, Ireland

[2] Tech Univ Munich, Theresienstr 90, D-80799 Munich, Germany

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2023年 / 87卷

基金：

瑞士国家科学基金会;

关键词：

Ring-linear code; Lee distance; Maximum Lee distance; Bounds; Constant weight codes; FINITE; SPARSENESS; GENERICITY; DISTANCE;

D O I：

10.1016/j.ffa.2022.102151

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we investigate known Singleton-like bounds in the Lee metric and characterize their extremal codes, which turn out to be very few. We then focus on Plotkin-like bounds in the Lee metric and present a new bound that extends and refines a previously known, and out-performs it in the case of non-free codes. We then compute the density of extremal codes with regard to the new bound. Finally we fill a gap in the characterization of Lee-equidistant codes. (c) 2022 Elsevier Inc. All rights reserved.

引用

页数：32

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