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
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页数：32
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