Cyclic codes over local Frobenius rings of order 16 | Zendy

Steven T. Dougherty | Zendy; Abidin Kaya | Zendy; Esengül Salturk | Zendy

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Cyclic codes over local Frobenius rings of order 16

Author(s) -

Steven T. Dougherty,

Abidin Kaya,

Esengül Salturk

Publication year - 2017

Publication title -

advances in mathematics of communications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.601

H-Index - 26

eISSN - 1930-5346

pISSN - 1930-5338

DOI - 10.3934/amc.2017005

Subject(s) - mathematics , order (exchange) , commutative property , generalization , cyclic code , binary number , gray code , discrete mathematics , combinatorics , pure mathematics , linear code , block code , algorithm , mathematical analysis , decoding methods , arithmetic , finance , economics

We study cyclic codes over commutative local Frobenius rings of order 16 and give their binary images under a Gray map which is a generalization of the Gray maps on the rings of order 4. We prove that the binary images of cyclic codes are quasi-cyclic codes of index 4 and give examples of cyclic codes of various lengths constructed from these techniques including new optimal quasi-cyclic codes.

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