The Kneser-Hecke-operator K is a linear operator defined on the complex vector space of formal linear combinations of the equivalence classes in a family of self-dual codes of fixed length. It maps a linear self-dual code C over a finite field to the formal sum of the equivalence classes of those self-dual codes that intersect C in a codimension 1 subspace.

These analogues of the well-known Hecke operators in the theory of modular forms act on weight-enumerators of codes,and hence on the invariant ring of the associated Clifford-Weil group.

In the coding theory case the possible eigenvalues of K can be calculated à priori and the corresponding eigenspaces are exactly the analogues of the spaces of Siegel cusp-forms.

This allows for instance to give the first coefficients of the Molien series of quite large groups (app. order 10⁷⁶)