Se p 20 05 An analogue of Hecke - operators in coding theory
نویسنده
چکیده
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.
منابع مشابه
Kneser-Hecke-operators in coding theory
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 d...
متن کاملSe p 20 09 Motives for elliptic modular groups
In order to study the arithmetic structure of elliptic modular groups which are the fundamental groups of compactified modular curves with cuspidal base points, these truncated Malcev Lie algebras and their direct sums are considered as elliptic modular motives. Our main result is a new theory of Hecke operators on these motives which gives a congruence relation to the Galois action, and a moti...
متن کامل2 2 Se p 20 05 GEOMETRIC REPRESENTATIONS OF GL ( n , R ) , CELLULAR HECKE ALGEBRAS AND THE EMBEDDING PROBLEM
We study geometric representations of GL(n, R) for a ring R. The structure of the associated Hecke algebras is analyzed and shown to be cellular. Multiplicities of the irreducible constituents of these representations are linked to the embedding problem of pairs of R-modules x ⊂ y.
متن کاملHecke Operators on the q-Analogue of Group Cohomology
We construct the q-analogue of a certain class of group cohomology and introduce the action of Hecke operators on such cohomology. We also show that such an action determines a representation of a Hecke ring in each of the associated group cohomology spaces. MSC 2000: 20G10, 11F60 (primary); 11F75, 18G99 (secondary)
متن کاملThe Selberg Trace Formula for Hecke Operators on Cocompact Kleinian Groups
We compute the Selberg trace formula for Hecke operators (also called the trace formula for modular correspondences) in the context of cocompact Kleinian groups with finite-dimentional unitary representations. We give some applications to the distribution of Hecke eigenvalues, and give an analogue of Huber’s theorem.
متن کامل