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- Title
On the equivalence of cyclic and quasi-cyclic codes over finite fields.
- Authors
Guenda, Kenza; Gulliver, T. Aaron
- Abstract
This paper studies the equivalence problem for cyclic codes of length pr and quasi-cyclic codes of length 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 the permutations by which two cyclic codes of prime power length are equivalent. This allows us to obtain an algorithm which solves the problem of equivalency for cyclic codes of length pr in polynomial time. Further, we characterize the set by which two quasi-cyclic codes of length prl can be equivalent, and prove that the affine group is one of its subsets.
- Subjects
MATHEMATICAL equivalence; CYCLIC codes; FINITE fields; GENERALIZABILITY theory; POLYNOMIALS
- Publication
Journal of Algebra Combinatorics Discrete Structures & Applications, 2017, Vol 4, Issue 3, p261
- ISSN
2148-838X
- Publication type
Article
- DOI
10.13069/jacodesmath.327375