The lengths of Hermitian Self-Dual Extended Duadic Codes

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.

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

References in corpus (1)

• Two-dimensional lattices with few distances

Cited by in corpus (6)

• Moser's mathemagical work on the equation 1^k+2^k+...+(m-1)^k=m^k
• On the Existence of Hermitian Self-Dual Extended Abelian Group Codes
• New Symmetric and Asymmetric Quantum Codes
• Good Integers and Applications in Coding Theory
• New MDS or near MDS self-dual codes over finite fields
• New MDS Euclidean and Hermitian self-dual codes over finite fields