Self-dual [62, 31, 12] and [64, 32, 12] codes with an automorphism of order 7

Abstract

This paper studies and classifies all binary self-dual $[62, 31, 12]$ and $[64, 32, 12]$ codes havingan automorphism of order 7 with 8 cycles. This classification is done by applying a method forconstructing binary self-dual codes with an automorphism of odd prime order $p$.There are exactly 8 inequivalent binary self-dual $[62, 31, 12]$ codes with an automorphism oftype $7-(8,6)$. As for binary $[64,32,12]$ self-dual codes with an automorphism of type $7-(8,8)$ thereare 44465 doubly-even and 557 singly-even such codes. Some of the constructed singly-even codes for both lengthshave weight enumerators for which the existence was not known before.