A new upper bound and optimal constructions of equi-difference conflict-avoiding codes on constant weight

TL;DR

This paper establishes a new upper bound for the size of equi-difference conflict-avoiding codes and provides three optimal constructions for different code lengths, enhancing multi-user communication efficiency.

Contribution

It introduces a novel upper bound and offers three new optimal constructions for equi-difference CACs, improving code design for various lengths.

Findings

New upper bound on maximum size of equi-difference CACs

Three optimal constructions for prime and two-prime lengths

Enhanced support for asynchronous multi-user communication

Abstract

Conflict-avoiding codes (CACs) have been used in multiple-access collision channel without feedback. The size of a CAC is the number of potential users that can be supported in the system. A code with maximum size is called optimal. The use of an optimal CAC enables the largest possible number of asynchronous users to transmit information efficiently and reliably. In this paper, a new upper bound on the maximum size of arbitrary equi-difference CAC is presented. Furthermore, three optimal constructions of equi-difference CACs are also given. One is a generalized construction for prime length $L=p$ and the other two are for two-prime length $L=pq$.