Extremal Binary and Ternary Codes of Length 60 with an Automorphism of Order 29 and a Generalization

Stefka Bouyuklieva,Darwin Villar,Javier De La Cruz

doi:10.3390/math10050748

Abstract

In this paper, all extremal Type I and Type III codes of length 60 with an automorphism of order 29 are classified up to equivalence. In both cases, it has been proven that there are three inequivalent codes. In addition, a new family of self-dual codes over non-binary fields is presented.

Highlights

Methods to construct and classify self-dual codes under the assumption that they have an automorphism of a given prime order were developed by Huffman and Yorgov [11–15]
For n = 60, extremal binary and ternary codes with automorphisms of order 29 exist, so we focus on this length
Let C ≤ Fnq be a linear code with a permutation automorphism σ ∈ Sym(n) of order r with c cycles of length r and f fixed points

Summary

Introduction

Methods to construct and classify self-dual codes under the assumption that they have an automorphism of a given prime order were developed by Huffman and Yorgov [11–15]. Many extremal self-dual codes of different lengths with different automorphisms were classified.

Results

Conclusion