English

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.

Keywords

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

R2 v1 2026-07-22T17:27:16.567Z