177 research outputs found
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 over a finite field to the
formal sum of the equivalence classes of those self-dual codes that intersect
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
-operator
On extremal self-dual ternary codes of length 48
All extremal ternary codes of length 48 that have some automorphism of prime
order are equivalent to one of the two known codes, the Pless code or
the extended quadratic residue code
On self-dual MRD codes
We determine the automorphism group of Gabidulin codes of full length and
characterise when these codes are equivalent to self-dual codes.Comment: Improved exposition according to the referees' comment
Hermitian modular forms congruent to 1 modulo p
For any natural number and any prime not
dividing there is a Hermitian modular form of arbitrary genus over
L:=\Q [\sqrt{-\ell}] that is congruent to 1 modulo which is a Hermitian
theta series of an -lattice of rank admitting a fixed point free
automorphism of order . It is shown that also for non-free lattices such
theta series are modular forms
Hecke actions on certain strongly modular genera of lattices
We calculate the action of some Hecke operators on spaces of modular forms
spanned by the Siegel theta-series of certain genera of strongly modular
lattices closely related to the Leech lattice. Their eigenforms provide
explicit examples of Siegel cusp forms
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