Quaternary Constant-Composition Codes with Weight Four and Distances Five or Six

TL;DR

This paper develops new methods to construct optimal quaternary constant-composition codes with weight four and minimum distances five or six, significantly advancing the understanding of their sizes and leaving only five lengths unresolved.

Contribution

It introduces novel constructions using group divisible codes and Room square approaches for these codes, filling gaps in existing knowledge.

Findings

Optimal code sizes determined for almost all lengths

Only five lengths remain unresolved in the classification

New construction techniques established for these codes

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 quaternary constant-composition codes with Hamming weight four and minimum distances five or six through group divisible codes and Room square approaches. The problem is solved leaving only five lengths undetermined. Previously, the results on the sizes of such quaternary constant-composition codes were scarce.