The [52, 26, 10] Binary Self-Dual Codes with an Automorphism of Order 7
✍ Scribed by W.Cary Huffman; Vladimir D. Tonchev
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 229 KB
- Volume
- 7
- Category
- Article
- ISSN
- 1071-5797
No coin nor oath required. For personal study only.
✦ Synopsis
All [52, 26,10] binary self-dual codes with an automorphism of order 7 are enumerated. Up to equivalence, there are 499 such codes. They have two possible weight enumerators, one of which has not previously arisen. 2001 Academic Press 1. INTRODUCTION In [1], Conway and Sloane present an upper bound on the minimum distance of Type I codes and list the possible weight enumerators for codes of length up to 72 which meet this bound. An open problem, examined by numerous authors (see [2}4 , 8, 11}13] for example), is to produce codes which possess weight enumerators in this list. A separate but related problem is to completely classify all self-dual codes which possess a particular type of automorphism; [7] surveys this work. In this paper we classify all [52, 26,10] self-dual codes with an automorphism of order 7. We show that there are 499 inequivalent codes and, in the process, discover that only two weight enumerators arise. One of these enumerators has not occurred before.