On the equivalence of cyclic and quasi-cyclic codes over finite fields

Journal of Algebra Combinatorics Discrete Structures and Applications

article

Kenza Guenda¹  T. Aaron Gulliver² 

[1] Faculty of Mathematics USTHB, University of Science and Technologyof Algiers;Department of Electrical and Computer Engineering, University of Victoria

关键词: Cyclic code;    Quasi-cyclic code;    Equivalence;    Automorphism;    Permutation;   

DOI  :  10.13069/jacodesmath.327375

学科分类：社会科学、人文和艺术（综合）

来源: Yildiz Technical University

【 摘 要 】

This paper studies the equivalence problem for cyclic codes of length prand quasi-cyclic codes oflength prl. In particular, we generalize the results of Huffman, Job, and Pless (J. Combin. Theory.A, 62, 183–215, 1993), who considered the special case p2. This is achieved by explicitly giving thepermutations by which two cyclic codes of prime power length are equivalent. This allows us to obtainan algorithm which solves the problem of equivalency for cyclic codes of length prin polynomial time.Further, we characterize the set by which two quasi-cyclic codes of length prl can be equivalent, andprove that the affine group is one of its subsets.

【 授权许可】

CC BY