Ternary near-extremal self-dual codes of lengths $36$, $48$ and $60$

TL;DR

This paper constructs new ternary near-extremal self-dual codes for lengths 36, 48, and 60, filling gaps in the known existence of such codes with specific weight enumerators.

Contribution

It introduces previously unknown ternary near-extremal self-dual codes for lengths 36, 48, and 60 with specific weight enumerators.

Findings

New codes for lengths 36, 48, and 60 discovered

Codes have weight enumerators previously not known to exist

Expands the classification of near-extremal self-dual codes

Abstract

For lengths $36$, $48$ and $60$, we construct new ternary near-extremal self-dual codes with weight enumerators for which no ternary near-extremal self-dual codes were previously known to exist.