On the Existence of Certain Optimal Self-Dual Codes with Lengths Between $74$ and $116$
Abstract
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 $100$.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2014
- DOI:
- 10.48550/arXiv.1405.7538
- arXiv:
- arXiv:1405.7538
- Bibcode:
- 2014arXiv1405.7538Z
- Keywords:
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- Computer Science - Information Theory
- E-Print:
- 15 pages, 5 tables