On the existence of certain optimal self-dual codes with lengths between 74 and 116

Tao Zhang¹ ; Jerod Michel¹ ; Tao Feng¹ ; Gennian Ge²

¹Zhejiang University
²Capital Normal University

The electronic journal of combinatorics, Tome 22 (2015) no. 4

Résumé

The existence of optimal binary self-dual codes is a long-standing research problem. In this paper, we present some results concerning the decomposition of binary self-dual codes with a dihedral automorphism group $D_{2p}$, where $p$ is a prime. These results are applied to construct new self-dual codes with length $78$ or $116$. We obtain $16$ inequivalent self-dual $[78,39,14]$ codes, four of which have new weight enumerators. We also show that there are at least $141$ inequivalent self-dual $[116,58,18]$ codes, most of which are new up to equivalence. Meanwhile, we give some restrictions on the weight enumerators of singly even self-dual codes. We use these restrictions to exclude some possible weight enumerators of self-dual codes with lengths $74$, $76$, $82$, $98$ and $100$.

Détail

DOI : 10.37236/5213

Classification : 94B05, 11T71
Mots-clés : self-dual code, automorphism, weight enumerator