Classification of binary self-dual [76, 38, 14] codes with an automorphism of order 9

TL;DR

This paper classifies all binary self-dual [76, 38, 14] codes with an automorphism of order 9, revealing six new codes with novel weight enumerator parameters, thus significantly expanding known code parameters.

Contribution

The authors classified all such codes with a specific automorphism, discovering six new codes with previously unknown weight enumerator parameters.

Findings

Six new self-dual [76, 38, 14] codes identified.

All codes have unique weight enumerator parameters.

More than doubling the known values of code parameters.

Abstract

Using the method for constructing binary self-dual codes with an automorphism of order square of a prime number we have classified all binary self-dual codes with length 76 having minimum distance $d=14$ and automorphism of order 9. Up to equivalence, there are six self-dual $[76, 38, 14]$ codes with an automorphism of type $9$-$(8,0,4)$. All codes obtained have new values of the parameter in their weight enumerator thus more than doubling the number of known values.