Hecke actions on certain strongly modular genera of lattices

Nebe, Gabriele; Teider, Maria

doi:10.1007/s00013-004-1288-4

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2006

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“…One missing concept in coding theory is that of Hecke-operators, which are an important tool in the theory of modular forms. Certain of these Hecke-operators may be expressed in terms of lattices (see [15], [14], [6]). The present paper translates this concept to coding theory.…”

Section: Introductionmentioning

confidence: 99%

Kneser— Hecke— operators in coding theory

Nebe

2006

Abh.Math.Semin.Univ.Hambg.

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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. MSC: 94B05, 11F60

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Section: Introductionmentioning

confidence: 99%