Division algebras and MRD codes from skew polynomials

被引：0

作者：

Thompson, D. ^{[1
]}

Pumpluen, S. ^{[2
]}

机构：

[1] 28 Coral Lane Newhall, Swadlincote DE11 0XU, England

[2] Univ Nottingham Univ Pk, Sch Math Sci, Nottingham NG7 2RD, England

来源：

GLASGOW MATHEMATICAL JOURNAL | 2023年 / 65卷 / 02期

关键词：

skew polynomial ring; skew polynomials; division algebras; MRD codes; RANK-METRIC CODES; IDEALS; SIGMA; RING; (F;

D O I：

10.1017/S001708952300006X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let D be a division algebra, finite-dimensional over its center, and R = D[t; s, d] a skew polynomial ring. Using skew polynomials f ? R, we construct division algebras and maximum rank distance codes consisting of matrices with entries in a noncommutative division algebra or field. These include Jha Johnson semifields, and the classes of classical and twisted Gabidulin codes constructed by Sheekey.

引用

页码：480 / 500

页数：21

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