In this paper, we give new constructions of disjoint difference families from Galois rings. The constructions are based on choosing cosets of the unit group of a subring in the Galois ring GR(p2, p2s). Two infinite families of disjoint difference families are obtained from the Galois rings GR(p2, p4n) and GR(22, 22s).

We demonstrate the equivalence of Kazama-Suzuki cosets G(m,n, k) and G(k, n,m) based on complex Grassmannians by proving that the corresponding conformal precosheaves are isomorphic. We also determine all the irreducible representations of the conformal precosheaves. §

In Quantum Computation and Lattice Problems [11] Oded Regev presented the first known connection between lattices and quantum computation, in the form of a quantum reduction from the poly(n)-unique shortest vector problem to the dihedral hidden subgroup problem by sampling cosets. This article contains a summary of Regev’s result.

Recently, entanglement-assisted quantum error correcting codes (EAQECCs) have been constructed by cyclic codes and negacyclic codes. In this paper, by analyzing the cyclotomic cosets in the defining set of constacyclic codes, we constructed three classes of new EAQECCs which satisfy the entanglement-assisted quantum Singleton bound. Besides, three classes of EAQECCs with maximal entanglement fr...

We introduced an application of the decomposition of a group into cosets of a subgroup to the theory of error detecting and correcting codes. The proposed approach is based on the general method for decoding linear codes known as syndrome decoding. Mathematics Subject Classification: 20A05; 20B05; 20B40

In this study, firstly, we interpret the level set, support, kernel for bipolar complex fuzzy (BCF) characteristic function, and BCF point. Then, subgroup, normal conjugate, normalizer cosets, abelian factor group. Furthermore, present associated examples theorems, prove these theorems. After that, image pre-image of subgroups under homomorphism related

<p>In this paper, we define the - -fuzzy subring and discussed various fundamental aspects of subrings. We introduce concept -level subset new fuzzy set prove that form a ring. ideal show all cosets Moreover, investigate properties homomorphic image subring.</p>