The classification of orthogonal arrays OA(2048,14,2,7) and some completely regular codes

Abstract: We describe the classification of orthogonal arrays OA$(2048,14,2,7)$, or, equivalently, completely regular ${14;2}$-codes in the $14$-cube ($30848$ equivalence classes). In particular, we find that there is exactly one almost-OA$(2048,14,2,7{+}1)$, up to equivalence. As derived objects, OA$(1024,13,2,6)$ ($202917$ classes) and completely regular ${12,2;2,12}$- and ${14, 12, 2; 2, 12, 14}$-codes in the $13$- and $14$-cubes, respectively, are also classified. Keywords: binary orthogonal array, completely regular code, binary 1-perfect code.