Polycyclic codes over Galois rings with applications to repeated-root constacyclic codes

Date

2013-01-01

Author

Lopez-Permouth, Sergio R.
Ozadam, Hakan
Özbudak, Ferruh
SZABO, Steve

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Cyclic, negacyclic and constacyclic codes are part of a larger class of codes called polycyclic codes; namely, those codes which can be viewed as ideals of a factor ring of a polynomial ring. The structure of the ambient ring of polycyclic codes over GR(p(a), m) and generating sets for its ideals are considered. It is shown that these generating sets are strong Groebner bases. A method for finding such sets in the case that a = 2 is given. This explicitly gives the Hamming distance of all cyclic codes of length p(s) over GR(p(2), m). The Hamming distance of certain constacyclic codes of length eta p(s) over F-pm is computed. A method, which determines the Hamming distance of the constacyclic codes of length eta p(s) over GR(p(a), m), where (eta, p) = 1, is described. In particular, the Hamming distance of all cyclic codes of length p(s) over GR(p(2), m) and all negacyclic codes of length 2p(s) over F-pm is determined explicitly. (c) 2012 Elsevier Inc. All rights reserved.

Subject Keywords

Linear codes, Torsion codes, Repeated-root cyclic codes, Groebner basis, Galois rings, Constacyclic codes, Cyclic codes

URI

https://hdl.handle.net/11511/38207

Journal

FINITE FIELDS AND THEIR APPLICATIONS

DOI

https://doi.org/10.1016/j.ffa.2012.10.002

Collections

Department of Mathematics, Article

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Citation Formats

S. R. Lopez-Permouth, H. Ozadam, F. Özbudak, and S. SZABO, “Polycyclic codes over Galois rings with applications to repeated-root constacyclic codes,” FINITE FIELDS AND THEIR APPLICATIONS, pp. 16–38, 2013, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38207.