Constructing Asymmetric Covering Codes by Tabu Search

A set \( C \subseteq \mathbb{F}_2^n \) is said to be an asymmetric covering code with radius \( R \) if every word \( x \in \mathbb{F}_2^n \) can be obtained by replacing \( 1 \) by \( 0 \) in at most \( R \) coordinates of a word in \( C \). In this paper, tabu search is employed in the search for good asymmetric covering codes of small length. Fifteen new upper bounds on the minimum size of such codes are obtained in the range \( n \leq 13 \).