Ordered covering arrays and upper bounds on covering codes

被引：1

作者：

Castoldi, Andre Guerino ^{[1
]}

Carmelo, Emerson Monte L. ^{[2
]}

Moura, Lucia ^{[3
]}

Panario, Daniel ^{[4
]}

Stevens, Brett ^{[4
]}

机构：

[1] Univ Tecnol Fed Parana, Dept Matemat, Pato Branco, PR, Brazil

[2] Univ Estadual Maringa, Dept Matemat, Maringa, PR, Brazil

[3] Univ Ottawa, Sch Elect Engn & Comp Sci, Ottawa, ON, Canada

[4] Carleton Univ, Sch Math & Stat, Ottawa, ON, Canada

来源：

JOURNAL OF COMBINATORIAL DESIGNS | 2023年 / 31卷 / 06期

基金：

加拿大自然科学与工程研究理事会;

关键词：

bounds on codes; covering array; covering code; Niederreiter-Rosenbloom-Tsfasman metric; ordered covering array; ordered orthogonal array; CONSTRUCTIONS; (T; M; S)-NETS;

D O I：

10.1002/jcd.21882

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This work shows several direct and recursive constructions of ordered covering arrays (OCAs) using projection, fusion, column augmentation, derivation, concatenation, and Cartesian product. Upper bounds on covering codes in Niederreiter-Rosenbloom-Tsfasman (shorten by NRT) spaces are also obtained by improving a general upper bound. We explore the connection between ordered covering arrays and covering codes in NRT spaces, which generalize similar results for the Hamming metric. Combining the new upper bounds for covering codes in NRT spaces and ordered covering arrays, we improve upper bounds on covering codes in NRT spaces for larger alphabets. We give tables comparing the new upper bounds for covering codes to existing ones.

引用

页码：304 / 329

页数：26

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