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
收藏
页码：480 / 500
页数：21
相关论文
共 50 条
  • [31] Skew Boolean algebras derived from generalized Boolean algebras
    Leech, Jonathan
    Spinks, Matthew
    ALGEBRA UNIVERSALIS, 2008, 58 (03) : 287 - 302
  • [32] LATTICES WITH SKEW-HERMITIAN FORMS OVER DIVISION ALGEBRAS AND UNLIKELY INTERSECTIONS
    Daw, Christopher
    Orr, Martin
    JOURNAL DE L ECOLE POLYTECHNIQUE-MATHEMATIQUES, 2023, 10 : 1097 - 1156
  • [33] Skew Boolean algebras derived from generalized Boolean algebras
    Jonathan Leech
    Matthew Spinks
    Algebra universalis, 2008, 58 : 287 - 302
  • [34] On soluble skew linear groups over finite-dimensional division algebras
    Wehrfritz, B. A. F.
    JOURNAL OF PURE AND APPLIED ALGEBRA, 2007, 209 (02) : 301 - 309
  • [35] Optimal quantum codes from additive skew cyclic codes
    Aydin, Nuh
    Abualrub, Taher
    DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2016, 8 (03)
  • [36] Factorization and root-finding for polynomials over division quaternion algebras
    Koprowski, Przemyslaw
    PROCEEDINGS OF THE INTERNATIONAL SYMPOSIUM ON SYMBOLIC & ALGEBRAIC COMPUTATION, ISSAC 2023, 2023, : 417 - 424
  • [37] New non-binary quantum codes from skew constacyclic and additive skew constacyclic codes
    Verma, Ram Krishna
    Prakash, Om
    Islam, Habibul
    Singh, Ashutosh
    EUROPEAN PHYSICAL JOURNAL PLUS, 2022, 137 (02):
  • [38] New non-binary quantum codes from skew constacyclic and additive skew constacyclic codes
    Ram Krishna Verma
    Om Prakash
    Habibul Islam
    Ashutosh Singh
    The European Physical Journal Plus, 137
  • [39] Optimal Ferrers diagram rank-metric codes from MRD codes
    Shuangqing Liu
    Designs, Codes and Cryptography, 2023, 91 : 3977 - 3993
  • [40] Optimal Ferrers diagram rank-metric codes from MRD codes
    Liu, Shuangqing
    DESIGNS CODES AND CRYPTOGRAPHY, 2023, 91 (12) : 3977 - 3993
12345