Some restrictions on the weight enumerators of near-extremal ternary self-dual codes and quaternary Hermitian self-dual codes

TL;DR

This paper establishes restrictions on the weight enumerators of certain near-extremal self-dual codes over ternary and quaternary fields, focusing on specific lengths divisible by 12 and 6 respectively.

Contribution

It provides new theoretical restrictions on weight enumerators for near-extremal self-dual codes of specified lengths, advancing understanding of their possible structures.

Findings

Restrictions on weight enumerators for ternary near-extremal self-dual codes of length 12m.

Restrictions on weight enumerators for quaternary near-extremal Hermitian self-dual codes of length 6m.

Applicable to codes with lengths m=3,4,5,6 for ternary and m=4,5,6 for quaternary codes.

Abstract

We give restrictions on the weight enumerators of ternary near-extremal self-dual codes of length divisible by $12$ and quaternary near-extremal Hermitian self-dual codes of length divisible by $6$. We consider the weight enumerators for which there is a ternary near-extremal self-dual code of length $12m$ for $m =3,4,5,6$. Also we consider the weight enumerators for which there is a quaternary near-extremal Hermitian self-dual code of length $6m$ for $m =4,5,6$.