Spinor groups and algebraic coding theory

Abstract The purpose of this paper is to explore the equivalence between the abelian subgroups of Ṽ(n), the “diagonal” extra-special 2-group of the compact, simple, simply-connected Lie group Spin(n), and the self-orthogonal linear binary codes of algebraic coding theory. In particular, the basic abstract structure theory of the abelian subgroups of Ṽ(n) is reflected in the distinction between ordinary self-orthogonal codes and even self-orthogonal codes. Work of Quillen on the equivariant cohomology of Spin(n) affects the classification of even self-orthogonal codes.