A Construction for Constant-Composition Codes

TL;DR

This paper introduces a new construction method for constant-composition codes using residue polynomials, improving existing bounds for certain parameters and providing near-optimal sizes for others.

Contribution

It generalizes previous constructions and establishes improved lower bounds for the maximal size of constant-composition codes, especially for d=3 and d=5.

Findings

Provides a lower bound for d=3 that improves previous results.

Establishes a new lower bound for d>3, notably for d=5, approaching optimal sizes.

Uses residue polynomials to construct codes with better parameters.

Abstract

By employing the residue polynomials, a construction of constant-composition codes is given. This construction generalizes the one proposed by Xing[16]. It turns out that when d=3 this construction gives a lower bound of constant-composition codes improving the one in [10]. Moreover, for d>3, we give a lower bound on maximal size of constant-composition codes. In particular, our bound for d=5 gives the best possible size of constant-composition codes up to magnitude.