An improvement of the Gilbert-Varshamov bound over nonprime fields

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Bassa, Alp and Beelen, Peter and Garcia, Arnaldo and Stichtenoth, Henning (2014) An improvement of the Gilbert-Varshamov bound over nonprime fields. IEEE Transactions on Information Theory, 60 (7). pp. 3859-3861. ISSN 0018-9448

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Abstract

The Gilbert-Varshamov bound guarantees the existence of families of codes over the finite field Fℓ with good asymptotic parameters. We show that this bound can be improved for all nonprime fields Fℓ with ℓ ≥ 49 , except possibly ℓ = 125. We observe that the same improvement even holds within the class of transitive codes and within the class of self-orthogonal codes.
Item Type: Article
Uncontrolled Keywords: AG codes, GV bound, towers of function fields
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: Henning Stichtenoth
Date Deposited: 26 Sep 2014 12:24
Last Modified: 02 Aug 2019 10:23
URI: https://research.sabanciuniv.edu/id/eprint/24353

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