Codes over an infinite family of algebras

Journal of Algebra Combinatorics Discrete Structures and Applications

article

Irwansyah¹  Intan Muchtadi-Alamsyah³  Ahmad Muchlis³  Aleams Barra³  Djoko Suprijanto⁴ 

[1] Institut Teknologi Bandung;Department of Mathematics, Universitas Mataram;Algebra Research Group, Institut Teknologi Bandung;Combinatorial Research Group, Institut Teknologi Bandung

关键词: Gray map;    Equivalence of codes;    Euclidean self-dual;    Hamming weight enumerator;    MacWilliams relation;    Invariant ring;   

DOI  :  10.13069/jacodesmath.284947

学科分类：社会科学、人文和艺术（综合）

来源: Yildiz Technical University

【 摘 要 】

In this paper, we will show some properties of codes over the ring Bk = Fp[v1, . . . , vk]/(v2i = vi, ∀i =1, . . . , k). These rings, form a family of commutative algebras over finite field Fp. We first discussabout the form of maximal ideals and characterization of automorphisms for the ring Bk. Then, wedefine certain Gray map which can be used to give a connection between codes over Bk and codes overFp. Using the previous connection, we give a characterization for equivalence of codes over Bk andEuclidean self-dual codes. Furthermore, we give generators for invariant ring of Euclidean self-dualcodes over Bk through MacWilliams relation of Hamming weight enumerator for such codes.

【 授权许可】

CC BY