The key objective of this paper is to study the cyclic codes over mixed alphabets on structure FqPQ, where P=Fq[v]⟨v3−α22v⟩ and Q=Fq[u,v]⟨u2−α12,v3−α22v⟩ are nonchain finite rings αi in Fq/{0} for i∈{1,2}, q=pm with m≥1 a positive integer p an odd prime. Moreover,with applications, we obtain better new quantum error-correcting (QEC) codes. For another application ring P, several optimal help Gr...

We show  that a projective maximal submodule of afinitely generated, regular, extending module is a directsummand. Hence, every finitely generated, regular, extendingmodule with projective maximal submodules is semisimple. As aconsequence, we observe that every regular, hereditary, extendingmodule is semisimple. This generalizes and simplifies a result of  Dung and   Smith. As another consequen...

Given a vector space V over a field (of size at least 1), we find a sharp bound for the minimal number (or in general, indexing set) of subspaces of a fixed (finite) codimension needed to cover V . If V is a finite set, this is related to the problem of partitioning V into subspaces. We also consider the analogous problem (involving proper subobjects only) for direct sums of cyclic monoids, cyc...

An association scheme is amorphous if it has as many fusion schemes as possible. Symmetric amorphous schemes were classified by A. V. Ivanov [A. V. Ivanov, Amorphous cellular rings II, in Investigations in algebraic theory of combinatorial objects, pages 39–49. VNIISI, Moscow, Institute for System Studies, 1985] and commutative amorphous schemes were classified by T. Ito, A. Munemasa and M. Yam...

A new phenacene-type molecule with five fused aromatic rings was synthesized: 2,7-didodecylphenanthro[2,1-b:7,8-b']dithiophene ((C12H25)2-i-PDT), with two terminal thiophene rings. Field-effect transistors (FETs) using thin films of this molecule were fabricated using various gate dielectrics, showing p-channel normally-off FET properties with field-effect mobilities (μ) greater than 1 cm2 V-1 ...

Abstract. A formal notion of a Typ T of a self-dual linear code over a finite left Rmodule V is introduced which allows to give explicit generators of a finite complex matrix group, the associated Clifford-Weil group C(T ) ≤ GL|V |(C), such that the complete weight enumerators of self-dual isotropic codes of Type T span the ring of invariants of C(T ). This generalizes Gleason’s 1970 theorem to...

The I-V characteristics of YBa2Cu3O7 rings are measured down to the subpicovolt level using a Hall magnetometry technique. Non-Ohmic response of the rings to an ac magnetic field is detected below a temperature TG . Fourier analysis of the data demonstrates appearance of higher harmonics up to order 9. The frequency and amplitude dependence of the harmonic susceptibilities is analyzed. The quas...

In this paper, we investigate cyclic codes over the ring Fp[u, v, w]〈u , v, w, uv− vu, vw − wv, uw − wu〉, where p is a prime number. Which is a part of family of Frobenius rings. We find a unique set of generators for these codes and characterize the free cyclic codes. We also study the rank and the Hamming distance of these codes. We also constructs some good p−ary codes as the Gray images of ...

I propose a model for the formation of the two outer rings of SN 1987A. The main new ingredient is a short-lived, few×10 years, intermediate wind, of velocity ∼ 100 km s and total mass of ∼ 10M⊙−few×10 M⊙, which is concentrated near the equatorial plane. This intermediate wind was formed during the few orbital periods when a binary companion entered the envelope of the progenitor of SN 1987a, w...