Construction of optimal Hermitian self-dual codes from unitary matrices

2019/11/24 by Lin Sok, Sok, Lin · 1 citation
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Computer and information sciences #Finite Group Theory Research #Information Theory (cs.IT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1911.10456

openalex publication_date 2019/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide an algorithm to construct unitary matrices over finite fields. We present various constructions of Hermitian self-dual code by means of unitary matrices, where some of them generalize the quadratic double circulant constructions. Many optimal Hermitian self-dual codes over large finite fields with new parameters are obtained. More precisely MDS or almost MDS Hermitian self-dual codes of lengths up to 18 are constructed over finite fields \F_q, where q=3²,4²,5²,7²,8²,9²,11²,13²,17²,19². Comparisons with classical constructions are made.

Citations

• A new upper bound on the minimal distance of self-dual codes

Cited by

• Hermitian Self-dual Twisted Generalized Reed-Solomon Codes

Related

• Construction of MDS self-dual codes from orthogonal matrices
• Explicit constructions of optimal linear codes with Hermitian hulls and their application to quantum codes
• Self-dual codes over GF(q) with symmetric generator matrices
• New MDS Euclidean and Hermitian self-dual codes over finite fields
• Special matrices over finite fields and their applications to quantum error-correcting codes