Cyclic codes and reducible additive equations

Date

2007-02-01

Author

Guneri, Cem
Özbudak, Ferruh

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We prove a Weil-Serre type bound on the number of solutions of a class of reducible additive equations over finite fields. Using the trace representation of cyclic codes, this enables us to write a general estimate for the weights of cyclic codes. We extend Woffmann's weight bound to a larger classes of cyclic codes. In particular, our result is applicable to any cyclic code over F-p and F-p2, where p is an arbitrary prime. Examples indicate that our bound performs very well against the Bose-Chaudhuri-Hocquenghem (BCH) bound and that it yields the exact minimum distance in some cases.

Subject Keywords

Library and Information Sciences, Information Systems, Computer Science Applications

URI

https://hdl.handle.net/11511/46926

Journal

IEEE TRANSACTIONS ON INFORMATION THEORY

DOI

https://doi.org/10.1109/tit.2006.889001

Collections

Department of Mathematics, Article

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Citation Formats

C. Guneri and F. Özbudak, “Cyclic codes and reducible additive equations,” IEEE TRANSACTIONS ON INFORMATION THEORY, pp. 848–853, 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46926.