Following Babai’s algorithm (Graph isomorphism in quasipolynomial time, arXiv:1512.03547v2, 2016) for the string problem, we determine that it is possible to write expressions of short length describing certain permutation cosets, including all subgroups. This feasible both original version and its CFSG-free version, by Babai (2016, §13.1) Pyber (A analysis GI algorithm, arXiv:1605.08266, 2016)...

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...

The binary primitive BCH codes are cyclic and constructed by choosing a subset of the cyclotomic cosets. Which is chosen determines dimension, minimum distance weight distribution code. We construct possible determine their coderate, true non-equivalent codes. A particular choice cosets gives which are, extended one bit, equivalent to Reed-Muller codes, known result from sixties. show that have...

The parameters of a q-ary MDS Euclidean self-dual codes are completely determined by its length and the construction with new has been widely investigated in recent years. In this paper, we give further study on via generalized Reed-Solomon (GRS) their extended codes. main idea our is to choose suitable evaluation points such that corresponding (extended) GRS self-dual. Firstly, consider set co...

The concepts of neutrosophic normal soft group, neutrosophic soft cosets, neutrosophic soft homomorphism are introduced and illustrated by suitable examples in this paper. Several related properties and structural characteristics are investigated. Some of their basic theorems are also established.

We study the double cosets of a Lie group by a compact Lie subgroup. We show that a Weil formula holds for double coset Lie hypergroups and show that certain representations of the Lie group lift to representations of the double coset Lie hypergroup. We characterize smooth (analytic) vectors of these lifted representations.