Optimal strongly conflict-avoiding codes of even length and weight three

TL;DR

This paper investigates the maximum size of strongly conflict-avoiding codes (SCACs) with even length and weight three, establishing upper bounds and showing how some optimal conflict-avoiding codes (CACs) can be adapted to construct optimal SCACs.

Contribution

It provides the first upper bounds for SCACs of even length and weight three and demonstrates a method to construct optimal SCACs from existing optimal CACs.

Findings

Established upper bounds on the size of SCACs of even length and weight three.

Showed that some optimal CACs can be used to construct optimal SCACs.

Enhanced understanding of the combinatorial structure of SCACs.

Abstract

Strongly conflict-avoiding codes (SCACs) are employed in a slot-asynchronous multiple-access collision channel without feedback to guarantee that each active user can send at least one packet successfully in the worst case within a fixed period of time. Assume all users are assigned distinct codewords, the number of codewords in an SCAC is equal to the number of potential users that can be supported. SCACs have different combinatorial structure compared with conflict-avoiding codes (CACs) due to additional collisions incurred by partially overlapped transmissions. In this paper, we establish upper bounds on the size of SCACs of even length and weight three. Furthermore, it is shown that some optimal CACs can be used to construct optimal SCACs of weight three.