Cyclic codes and reducible additive equations

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Güneri, Cem and Özbudak, Ferruh (2007) Cyclic codes and reducible additive equations. IEEE Transactions On Information Theory, 53 (2). pp. 848-853. ISSN 0018-9448

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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 Wolfmann's weight bound to a larger classes of cyclic codes. In particular, our result is applicable to any cyclic code over Fp and Fp 2, 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.
Item Type: Article
Uncontrolled Keywords: cyclic code; reducible additive equation; trace representation; Weil-Serre bound; Wolfmann's bound
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Engineering and Natural Sciences
Depositing User: Cem Güneri
Date Deposited: 08 Dec 2006 02:00
Last Modified: 25 May 2011 14:13

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