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

#### Kenza GUENDA [1] , T. Aaron GULLİVER [2]

This paper studies the equivalence problem for cyclic codes of length $p^r$ and quasi-cyclic codes of length $p^rl$. In particular, we generalize the results of Huffman, Job, and Pless (J. Combin. Theory. A, 62, 183--215, 1993), who considered the special case $p^2$. 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 $p^r$ in polynomial time. Further, we characterize the set by which two quasi-cyclic codes of length $p^rl$ can be equivalent, and prove that the affine group is one of its subsets.
Cyclic code, Quasi-cyclic code, Equivalence, Automorphism, Permutation
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Subjects Engineering Articles Orcid: 0000-0002-1482-7565Author: Kenza GUENDA Orcid: 0000-0001-9919-0323Author: T. Aaron GULLİVER Publication Date : September 15, 2017
 Bibtex @research article { jacodesmath327375, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {}, publisher = {Yildiz Technical University}, year = {2017}, volume = {4}, pages = {261 - 269}, doi = {10.13069/jacodesmath.327375}, title = {On the equivalence of cyclic and quasi-cyclic codes over finite fields}, key = {cite}, author = {Guenda, Kenza and Gulli̇ver, T. Aaron} } APA Guenda, K , Gulli̇ver, T . (2017). On the equivalence of cyclic and quasi-cyclic codes over finite fields . Journal of Algebra Combinatorics Discrete Structures and Applications , 4 (3) , 261-269 . DOI: 10.13069/jacodesmath.327375 MLA Guenda, K , Gulli̇ver, T . "On the equivalence of cyclic and quasi-cyclic codes over finite fields" . Journal of Algebra Combinatorics Discrete Structures and Applications 4 (2017 ): 261-269 Chicago Guenda, K , Gulli̇ver, T . "On the equivalence of cyclic and quasi-cyclic codes over finite fields". Journal of Algebra Combinatorics Discrete Structures and Applications 4 (2017 ): 261-269 RIS TY - JOUR T1 - On the equivalence of cyclic and quasi-cyclic codes over finite fields AU - Kenza Guenda , T. Aaron Gulli̇ver Y1 - 2017 PY - 2017 N1 - doi: 10.13069/jacodesmath.327375 DO - 10.13069/jacodesmath.327375 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 261 EP - 269 VL - 4 IS - 3 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.327375 UR - https://doi.org/10.13069/jacodesmath.327375 Y2 - 2017 ER - EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications On the equivalence of cyclic and quasi-cyclic codes over finite fields %A Kenza Guenda , T. Aaron Gulli̇ver %T On the equivalence of cyclic and quasi-cyclic codes over finite fields %D 2017 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 4 %N 3 %R doi: 10.13069/jacodesmath.327375 %U 10.13069/jacodesmath.327375 ISNAD Guenda, Kenza , Gulli̇ver, T. Aaron . "On the equivalence of cyclic and quasi-cyclic codes over finite fields". Journal of Algebra Combinatorics Discrete Structures and Applications 4 / 3 (September 2017): 261-269 . https://doi.org/10.13069/jacodesmath.327375 AMA Guenda K , Gulli̇ver T . On the equivalence of cyclic and quasi-cyclic codes over finite fields. Journal of Algebra Combinatorics Discrete Structures and Applications. 2017; 4(3): 261-269. Vancouver Guenda K , Gulli̇ver T . On the equivalence of cyclic and quasi-cyclic codes over finite fields. Journal of Algebra Combinatorics Discrete Structures and Applications. 2017; 4(3): 261-269.

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