Optimal equi-difference conflict-avoiding codes of weight four

摘要

A conflict-avoiding code (CAC) of length and weight is defined as a family of -subsets (called codewords) of , the ring of residues modulo , such that for any , where . A code in CACs of length and weight is called an equi-difference code if every codeword has the form . A code in CACs of length and weight is said to be optimal if has the maximum number of codewords. In this article, we investigate sizes and constructions of optimal codes in equi-difference CACs of weight four by using properly defined directed graphs. As a consequence, several series of infinite number of optimal equi-difference CACs are also provided.