On extremal self-dual ternary codes of length 48

TL;DR

This paper classifies extremal self-dual ternary codes of length 48 with automorphisms of prime order p ≥ 5, showing they are equivalent to only two known codes, the Pless code or the extended quadratic residue code.

Contribution

It proves that all such codes with prime automorphisms of order p ≥ 5 are equivalent to two well-known codes, confirming their uniqueness in this context.

Findings

All extremal self-dual ternary codes of length 48 with prime automorphisms p ≥ 5 are equivalent to the Pless or extended quadratic residue code.

The classification reduces the possibilities to these two known codes.

Automorphisms of prime order p ≥ 5 do not produce new codes beyond these two.

Abstract

All extremal ternary codes of length 48 that have some automorphism of prime order $p\geq 5$ are equivalent to one of the two known codes, the Pless code or the extended quadratic residue code.