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.
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页码：480 / 500
页数：21
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