On Binary Codes That Are Maximal Totally Isotropic Subspaces with Respect to an Alternating Form

Abstract

Self-dual binary linear codes have been extensively studied and classified for length n <= 40. However, little attention has been paid to linear codes that coincide with their orthogonal complement when the underlying inner product is not the dot product. In this paper, we introduce an alternating form defined on F_2^n and study codes that are maximal totally isotropic with repsect to this form. We classify such codes for n <= 24 and present a MacWilliams-type identity which relates the weight enumerator of a linear code and that of its orthogonal complement with respect to our alternating inner product. As an application, we derive constraints on the weight enumerators of maximal totally isotropic codes.