The lengths of Hermitian Self-Dual Extended Duadic Codes
Combinatorics
2007-05-23 v2 Number Theory
Abstract
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.
Cite
@article{arxiv.math/0511295,
title = {The lengths of Hermitian Self-Dual Extended Duadic Codes},
author = {Lilibeth Dicuangco and Pieter Moree and Patrick Sole},
journal= {arXiv preprint arXiv:math/0511295},
year = {2007}
}
Comments
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. Some small changes have been made