In this paper, we construct two infinite families of binary linear codes associated with double cosets with respect to certain maximal parabolic subgroup of the symplectic group Sp(2n, q). Here q is a power of two. Then we obtain an infinite family of recursive formulas for the power moments of Kloosterman sums and those of 2-dimensional Kloosterman sums in terms of the frequencies of weights i...

In this paper we show how string rewriting methods can be applied to give a new method of computing double cosets. Previous methods for double cosets were enumerative and thus restricted to finite examples. Our rewriting methods do not suffer this restriction and we present some examples of infinite double coset systems which can now easily be solved using our approach. Even when both enumerati...

Two efficient computer implemented algorithms are presented -=. :'or explicitly constructing all distinct labelings of a graph G :;ith a set of (not necessarily distinct) labels L , given the _;ymmetry group B of G . Two recursive reductions of the problem ,?_rld a precomputation involving certain orbits of stabilizer subgroups q--e the LAtechniques used by the algorithm. Moreover, for each la3...

The Todd-Coxeter algorithm described in [13] remains a primary reference for coset enumeration programs. It may be viewed as a means of constructing permutation representations of finitely presented groups. A number of effective computer programs for singlecoset enumeration have been described, see, for example, [2, 7, 8]. Enumerating double cosets, rather than single cosets, gives substantial ...

In this survey article, we focus on graphs and complexes arising from quotients of the Bruhat-Tits buildings associated to PGL2(F ) and PGL3(F ), respectively. As such, the combinatorial objects, like vertices, edges and chambers, are parametrized algebraically by cosets, and the combinatorial adjacency operators can be interpreted as operators supported on suitable double cosets acting on cert...

In this paper, we construct eight infinite families of ternary linear codes associated with double cosets with respect to certain maximal parabolic subgroup of the special orthogonal group SO − (2n, q). Here q is a power of three. Then we obtain four infinite families of recursive formulas for power moments of Kloosterman sums with square arguments and four infinite families of recursive formul...

Let $\mathbb F$ be a finite field. Consider direct sum $V$ of an infinite number copies F$, consider the dual space $V^\diamond$, i.~e., product F$. ${\mathbb V}=V\oplus V^\diamond$. The object paper is group $\mathbf{GL}$ continuous linear operators in V$. We reduce theory unitary representations to projective certain category whose morphisms are relations finite-dimensional spaces over In fac...