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.

v2: revised, corrected, representation of the almost-OA(2048,14,2,7+1) updated; v3: accepted version (minor revision)