The lengths of Hermitian Self-Dual Extended Duadic Codes

Details The lengths of Hermitian Self-Dual Extended Duadic Codes The lengths of Hermitian Self-Dual Extended Duadic Codes

2005-11-11

arxiv.org/abs/math/0511295v2

J. Pure Appl. Algebra 209 (2007), 223-237

Mathematics

Combinatorics

To appear in the Journal of Pure and Applied Algebra. 21 pages and 1 Table. Corollary 4.9 and Theorem 5.8 have been added. Som

Scientific paper

10.1016/j.jpaa.2006.05.024

Duadic codes are a class of cyclic codes that generalizes quadratic residue codes from prime to composite lengths. For every prime power q, we characterize the integers n such that over the finite field with q^2 elements there is a duadic code of length n having an Hermitian self-dual parity-check extension. We derive using analytic number theory asymptotic estimates for the number of such n as well as for the number of lengths for which duadic codes exist.

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