We study the coset weight distributions of the 3-error-correcting binary narrowsense BCH-codes and of their extensions, whose lengths are, respectively, 2m − 1 and 2m, m odd. We prove that all weight distributions are known as soon as those of the cosets of minimum weight 4 of the extended code are known. We point out that properties of the cosets which are orphans yield interesting properties ...

We give a one-to-one correspondence between classes of density matrices under local unitary invariance and the double cosets of unitary groups. We show that the interrelationship among classes of local unitary equivalent multi-partite mixed states is independent from the actual values of the eigenvalues and only depends on the multiplicities of the eigenvalues. The interpretation in terms of ho...

Quadratic residue codes have been one of the most important classes of algebraic codes. They have been generalized into duadic codes and quadratic double circulant codes. In this paper we introduce a new subclass of double circulant codes, called duadic double circulant codes, which is a generalization of quadratic double circulant codes for prime lengths. This class generates optimal self-dual...

The kan package was originally implemented in 1997 using the GAP 3 language, to compute induced actions of categories, when the first author was studying for a Ph.D. in Bangor. This reduced version only provides functions for the computation of normal forms of representatives of double cosets of finitely presented groups. Bug reports, suggestions and comments are, of course, welcome. Please con...

LetG be a finite group of Lie type (e.g. GLn(Fq)) and U a maximal unipotent subgroup of G. If ψ is a linear character of U , then the unipotent Hecke algebra isHψ = EndCG(Ind G U (ψ)). Unipotent Hecke algebras have a natural basis coming from double cosets of U in G. This paper describes relations for reducing products of basis elements, and gives a detailed description of the implications in t...

If G is a split reductive group and B a Borel subgroup then G is the disjoint union of the BwB as w ranges over the Weyl group of a maximal torus in B. The closure of BwB is the union of certain double cosets BxB, where the x that occur can be characterized in purely combinatorial terms. Somewhat surprisingly, this combinatorial definition may be extended to define the Bruhat closure operation ...

Let M be a graph manifold. We prove that fundamental groups of embedded incompressible surfaces in M are separable in π1M , and that the double cosets for crossing surfaces are also separable. We deduce that if there is a ‘sufficient’ collection of surfaces in M , then π1M is virtually the fundamental group of a special non-positively curved cube complex. We provide a sufficient collection for ...

Introduction Let G be a connected reductive group over an algebraically closed eld k; let B G be a Borel subgroup and K G a closed subgroup. Assume that K is a spherical subgroup of G, that is, the number of K-orbits in the ag variety G=B is nite; equivalently, the set KnG=B of (K; B)-double cosets in G is nite. Then the following problems arise naturally.