Kneser-Hecke-operators in coding theory

Details Kneser-Hecke-operators in coding theory Kneser-Hecke-operators in coding theory

2005-09-21

arxiv.org/abs/math/0509474v2

Mathematics

Number Theory

Scientific paper

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 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. The eigenspaces of this self-adjoint linear operator may be described in terms of a coding-theory analogue of the Siegel $\Phi $-operator.

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