New examples of self-dual near-extremal ternary codes of length 48 derived from 2-(47,23,11) designs

TL;DR

This paper constructs new self-dual near-extremal ternary codes of length 48 using symmetric 2-(47,23,11) designs, expanding the known range of the number of minimum weight codewords.

Contribution

It introduces a novel construction method for these codes based on symmetric designs with specific automorphism groups, increasing the known possible values of A_{12}.

Findings

Constructed codes for 150 new A_{12} values.

Extended the known spectrum of near-extremal ternary codes.

Demonstrated the use of symmetric 2-designs in code construction.

Abstract

In a recent paper [M. Araya, M. Harada, Some restrictions on the weight enumerators of near-extremal ternary self-dual codes and quaternary Hermitian self-dual codes, Des. Codes Cryptogr., 91 (2023), 1813--1843], Araya and Harada gave examples of self-dual near-extremal ternary codes of length 48 for $145$ distinct values of the number $A_{12}$ of codewords of minimum weight 12, and raised the question about the existence of codes for other values of $A_{12}$. In this note, we use symmetric 2-$(47,23,11)$ designs with an automorphism group of order 6 to construct self-dual near-extremal ternary codes of length 48 for $150$ new values of $A_{12}$.