A General Upper Bound on the Size of Constant-Weight Conflict-Avoiding Codes

TL;DR

This paper establishes a universal upper bound on the size of constant-weight conflict-avoiding codes, applicable across all code lengths and weights, and confirms the optimality of several known constructions.

Contribution

It introduces a new general upper bound for conflict-avoiding codes and proves the optimality of existing constructions for all Hamming weights.

Findings

New upper bound valid for all code lengths and weights

Existing constructions are optimal for all Hamming weights

Supports more users in multiple-access channels

Abstract

Conflict-avoiding codes are used in the multiple-access collision channel without feedback. The number of codewords in a conflict-avoiding code is the number of potential users that can be supported in the system. In this paper, a new upper bound on the size of conflict-avoiding codes is proved. This upper bound is general in the sense that it is applicable to all code lengths and all Hamming weights. Several existing constructions for conflict-avoiding codes, which are known to be optimal for Hamming weights equal to four and five, are shown to be optimal for all Hamming weights in general.