Classification of Resolvable $2$-$(14,7,12)$ and $3$-$(14,7,5)$ Designs

Abstract

The resolvable $2$-$(14,7,12)$ designs are classified in a computer search: there are 1,363,486 such designs, 1,360,800 of which have trivial full automorphism group. Since every resolvable $2$-$(14,7,12)$ design is also a resolvable $3$-$(14,7,5)$ design and vice versa, the latter designs are simultaneously classified. The computer search utilizes the fact that these designs are equivalent to certain binary equidistant codes, and the classification is carried out with an orderly algorithm that constructs the designs point by point. As a partial check, a subset of these designs is constructed with an alternative approach by forming the designs one parallel class at a time.