Weil-Serre type bounds for cyclic codes

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Güneri, Cem and Özbudak, Ferruh (2008) Weil-Serre type bounds for cyclic codes. IEEE Transactions On Information Theory, 54 (12). pp. 5381-5395. ISSN 0018-9448

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We give a new method in order to obtain Weil-Serre type bounds on the minimum distance of arbitrary cyclic codes over $\mathbb{F}_{p^e}$ of length coprime to $p$, where $e\geq 1$ is an arbitrary integer. In an earlier paper we obtained Weil-Serre type bounds for such codes only when $e = 1$ or $e = 2$ using lengthy explicit factorizations, which seems hopeless to generalize. The new method avoids such explicit factorizations and it produces an effective alternative. Using our method we obtain Weil-Serre type bounds in various cases. By examples we show that our bounds perform very well against Bose-Chaudhuri-Hocquenghem bound and they yield the exact minimum distance in some cases.
Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Depositing User: Cem Güneri
Date Deposited: 06 Dec 2008 14:26
Last Modified: 26 Apr 2022 08:25
URI: https://research.sabanciuniv.edu/id/eprint/10914

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