Classification of Binary Self-Dual [48,24,10] Codes with an Automorphism of Odd Prime Order

Stefka Bouyuklieva; Nikolay Yankov; Jon-Lark Kim

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arXiv · 1201.4334

Classification of Binary Self-Dual [48,24,10] Codes with an Automorphism of Odd Prime Order

Stefka Bouyuklieva·Nikolay Yankov·Jon-Lark Kim

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Abstract

The purpose of this paper is to complete the classification of binary self-dual [48,24,10] codes with an automorphism of odd prime order. We prove that if there is a self-dual [48, 24, 10] code with an automorphism of type p-(c,f) with p being an odd prime, then p=3, c=16, f=0. By considering only an automorphism of type 3-(16,0), we prove that there are exactly 264 inequivalent self-dual [48, 24, 10] codes with an automorphism of odd prime order, equivalently, there are exactly 264 inequivalent cubic self-dual [48, 24, 10] codes.

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Stefka Bouyuklieva, Nikolay Yankov, Jon-Lark Kim. 2012-01-20. Classification of Binary Self-Dual [48,24,10] Codes with an Automorphism of Odd Prime Order. https://arxiv.org/abs/1201.4334

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