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Kneser-Hecke-operators in coding theory

Gabriele Nebe
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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 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 $Φ$-operator.

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Gabriele Nebe. 2006-07-18. Kneser-Hecke-operators in coding theory. https://arxiv.org/abs/math/0509474

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