Kneser— Hecke— operators in coding theory

Abstract

The Kneser-Hecke-operator is a linear operator defined on the complex vector space spanned by the equivalence classes of a family of self-dual codes of fixed length. It maps a linear self-dual codeC over a finite field to the formal sum of the equivalence classes of those self-dual codes that intersectC in a codi-mension 1 subspace. The eigenspaces of this self-adjoint linear operator may be described in terms of a coding-theory analogue of the Siegel Φ-operator.