Self-Dual [24, 12, 8] Quaternary Codes with a Nontrivial Automorphism of Order 3

Abstract

All (Hermitian) self-dual [24,12,8] quaternary codes which have a non--trivial automorphism of order 3 are obtained up to equivalence. There exist exactly 205 inequivalent such codes. The codes under consideration are optimal, self-dual, and have the highest possible minimum distance for this length.2002 Elsevier Science

Quaternary Hermitian self-dual codes of lengths 26, 32, 36, 38 and 40 from modifications of well-known circulant constructions

“…The code constructed by Theorem 3.4 is equivalent one of those constructed by Theorem 3.1. The number of inequivalent Hermitian self-dual [28,14,10]-codes we find does not improve on the current bound [18].…”

“…Using Theorem 3.1 and 3.4, we find 3 and 1 Hermitian self-dual [28,14,10]-codes, respectively. The code constructed by Theorem 3.4 is equivalent one of those constructed by Theorem 3.1.…”

“…Each code constructed by Theorem 3.4 is equivalent to one of those constructed by Theorem 3.1. All of the constructed Hermitian self-dual [24,12,8]-codes possess weight enumerators which have been previously known to exist [4,29,15,22,28].…”

“…A complete classification of quaternary Hermitian self-dual codes for lengths up to 22 is given in [17]. Optimal quaternary Hermitian self-dual codes of length 24 possessing non-trivial automorphisms of order ≥ 3 are classified in [29,28]. Extremal quaternary Hermitian self-dual codes of length 28 possessing non-trivial odd order automorphisms are classified in [18,19].…”