Criteria to design good space-time trellis codes (STTCs) have been already developed in previous publications. However, the computation of the best STTCs is time-consuming because a long exhaustive or systematic computing search is required, especially for a high number of states and/or transmit antennas. In order to reduce the search time, an efficient method must be employed to generate the S...

Abstract The extended coset leader weight enumerator of the generalized Reed–Solomon $$[q+1,q-3,5]_q$$ [ q + 1 , - 3 5 ] code is...

We describe an implementation of a genetic algorithm on partially commutative groups and apply it to the double coset search problem on a subclass of groups. This transforms a combinatorial group theory problem to a problem of combinatorial optimisation. We obtain a method applicable to a wide range of problems and give results which indicate good behaviour of the genetic algorithm, hinting at ...

The paper begins by giving an algebraic structure on a set of coset representatives for the left action of a subgroup on a group. From this we construct a non-trivially associated tensor category. Also a double construction is given, and this allows the construction of a non-trivially associated braided tensor category. In this category we explicitly reconstruct a braided Hopf algebra, whose re...

We construct and study two series of curves whose Jacobians admit complex multiplication. The curves arise as quotients of Galois coverings of the projective line with Galois group metacyclic groups Gq,3 of order 3q with q ≡ 1 mod 3 an odd prime, and Gm of order 2 . The complex multiplications arise as quotients of double coset algebras of the Galois groups of these coverings. We work out the C...

We analyze the hypermultiplet moduli space describing the universal sector of type IIA theory compactified on a Calabi-Yau threefold. The classical moduli space is described in terms of the coset SU(2, 1)/U(2). The flux quantization condition of the antisymmetric tensor field of M-theory implies discrete identifications for the scalar fields describing this four-dimensional quaternionic geometr...

This article presents the examination of the possibility that group Eg' F21 operates on a symmetric design with parameters (133,33,8) as its automorphism group. The method based on coset enumeration in group is used.

We construct smallest known trivalent graphs for girths 16 and 18. One construction uses voltage graphs, and the other coset enumeration techniques for group presentations. AMS Subject Classifications: 05C25, 05C35

We present a global analysis of the geometries that arise in non-compact current algebra (or gauged WZW) coset models of strings and particles propagating in curved space-time. The simplest case is the 2d black hole. In higher dimensions these geometries describe new and much more complex singularities. For string and particle theories (defined in the text) we introduce general methods for iden...

In symmetric groups, viewed as Coxeter groups, we show that the set of elements of minimal length in a double sided cell is the set of elements of maximal length in conjugated parabolic (i.e. Young) subgroups. We also give an interpretation of this set with tableau, using the RobinsonSchensted correspondance. We show also that the set of elements of maximal length in a two sided cell is the set...