Optimal Ternary Constant-Composition Codes with Weight Four and Distance Six

TL;DR

This paper investigates the construction of optimal ternary constant-composition codes with weight four and minimum distance six, extending known results to larger code lengths and addressing unresolved cases.

Contribution

It introduces new constructions for optimal codes with weight four and distance six, expanding the range of known optimal code lengths beyond 10.

Findings

Optimal codes constructed for most lengths with few exceptions

Extended the range of known code lengths for these codes

Provided new methods for code construction

Abstract

The sizes of optimal constant-composition codes of weight three have been determined by Chee, Ge and Ling with four cases in doubt. Group divisible codes played an important role in their constructions. In this paper, we study the problem of constructing optimal ternary constant-composition codes with Hamming weight four and minimum distance six. The problem is solved with a small number of lengths undetermined. The previously known results are those with code length no greater than 10.