ON PERFECT POSET CODES

被引：1

作者：

Panek, Luciano ^{[1
]}

Pinheiro, Jerry Anderson ^{[2
]}

Alves, Marcelo Muniz ^{[3
]}

Firer, Marcelo ^{[4
]}

机构：

[1] State Univ West Parana, Ctr Exact Sci & Engn, Foz Do Iguacu, Parana, Brazil

[2] Fed Univ Latin Amer Integrat, ILACVN, Foz Do Iguacu, Parana, Brazil

[3] Univ Fed Parana, Polytech Ctr, Dept Math, Curitiba, Parana, Brazil

[4] Univ Estadual Campinas, IMECC, Dept Math, Campinas, SP, Brazil

来源：

ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2020年 / 14卷 / 03期

基金：

巴西圣保罗研究基金会;

关键词：

Poset codes; poset metrics; perfect codes; Hamming codes; LINEAR CODES; METRICS;

D O I：

10.3934/amc.2020061

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We consider on F-q(n) metrics determined by posets and classify the parameters of 1-perfect poset codes in such metrics. We show that a code with same parameters of a 1-perfect poset code is not necessarily perfect, however, we give necessary and sufficient conditions for this to be true. Furthermore, we characterize the unique way up to a labeling on the poset, considering some conditions, to extend an r-perfect poset code over F-q(n) to an r-perfect poset code over F-q(n+m).

引用

页码：477 / 489

页数：13

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