This paper aims to study the Smarandache cosets and derive some interesting results about them. We prove the classical Lagranges theorem for Smarandache semigroup is not true and that there does not exist a one-to-one correspondence between any two right cosets. We also show that the classical theorems cannot be extended to all Smarandache semigroups. This leads to the definition of Smarandache...

A description is given of how to construct (0, 2) supersymmetric conformal field theories as coset models. These models may be used as non–trivial backgrounds for Heterotic String Theory. They are realised as a combination of an anomalously gauged Wess–Zumino–Witten model, right–moving supersymmetric fermions, and left–moving current algebra fermions. Requiring the sum of the gauge anomalies fr...

We study the weight distributions of cosets of the first-order Reed–Muller code (1 ) for odd , whose minimum weight is greater than or equal to the so-called quadratic bound. Some general restrictions on the weight distribution of a coset of (1 ) are obtained by partitioning its words according to their weight divisibility. Most notably, we show that there are exactly five weight distributions ...

In this paper, we construct four infinite families of ternary linear codes associated with double cosets in O(2n+1, q) with respect to certain maximal parabolic subgroup of the special orthogonal group SO(2n + 1, q). Here q is a power of three. Then we obtain two infinite families of recursive formulas , the one generating the power moments of Kloosterman sums with " trace nonzero square argume...

Suppose q is a prime power and f ∈ Fq[x] is a univariate polynomial with exactly t nonzero terms and degree <q−1. To establish a finite field analogue of Descartes’ Rule, Bi, Cheng and Rojas (2013) proved an upper bound of 2(q − 1) t−2 t−1 on the number of cosets in F∗ q needed to cover the roots of f in F∗ q . Here, we give explicit f with root structure approaching this bound: For q a t power...

In this paper, we construct an infinite family of binary linear codes associated with double cosets with respect to a certain maximal parabolic subgroup of the orthogonal group O(2n+1, q). Here q is a power of two. Then we obtain an infinite family of recursive fomulas generating the odd power moments of Kloosterman sums with trace one arguments in terms of the frequencies of weights in the cod...