A Bound on the Minimum Distance of Quasi-cyclic Codes

Date

2012-01-01

Author

Gueneri, Cem
Özbudak, Ferruh

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We give a general lower bound for the minimum distance of q-ary quasi-cyclic codes of length ml and index l, where m is relatively prime to q. The bound involves the minimum distances of constituent codes of length l as well as the minimum distances of certain cyclic codes of length m which are related to the fields over which the constituents are defined. We present examples which show that the bound is sharp in many instances. We also compare the performance of our bound against the bounds of Lally and Esmaeili-Yari.

Subject Keywords

Quasi-cyclic code, Trace representation, Constituent code

URI

https://hdl.handle.net/11511/37360

Journal

SIAM JOURNAL ON DISCRETE MATHEMATICS

DOI

https://doi.org/10.1137/120865823

Collections

Department of Mathematics, Article

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Citation Formats

C. Gueneri and F. Özbudak, “A Bound on the Minimum Distance of Quasi-cyclic Codes,” SIAM JOURNAL ON DISCRETE MATHEMATICS, pp. 1781–1796, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/37360.