Identification of 2-arylquinazolines with alkyl-polyamine motifs as potent antileishmanial agents: Synthesis and biological evaluation studies

2-Arylquinazolines with a range of alkyl polyamines as side chain/ring functional motifs at 4th-position were considered for antileishmanial study with the rationale that related heterocyclic scaffolds and the polyamine functionalities...

On classification of finite commutative chain rings

<abstract><p>Let $ R $ be a finite commutative chain ring with invariants $ p, n, r, k, m. $ It is known that $ R $ is an extension over a Galois ring $ GR(p^n, r) $ by an Eisenstein polynomial of some degree $ k $. If $ p\nmid k, $ the enumeration of such rings is known. However, when $ p\mid k $, relatively little is known about the classification of these rings. The main purpose of this article is to investigate the classification of all finite commutative chain rings with given invariants $ p, n, r, k, m $ up to isomorphism when $ p\mid k. $ Based on the notion of j-diagram initiated by Ayoub, the number of isomorphism classes of finite (complete) chain rings with $ (p-1)\nmid k $ is determined. In addition, we study the case $ (p-1)\mid k, $ and show that the classification is strongly dependent on Eisenstein polynomials not only on $ p, n, r, k, m. $ In this case, we classify finite (incomplete) chain rings under some conditions concerning the Eisenstein polynomials. These results yield immediate corollaries for p-adic fields, coding theory and geometry.</p></abstract>

Constacyclic Codes over Finite Chain Rings of Characteristic p

Let R be a finite commutative chain ring of characteristic p with invariants p,r, and k. In this paper, we study λ-constacyclic codes of an arbitrary length N over R, where λ is a unit of R. We first reduce this to investigate constacyclic codes of length ps (N=n1ps,p∤n1) over a certain finite chain ring CR(uk,rb) of characteristic p, which is an extension of R. Then we use discrete Fourier transform (DFT) to construct an isomorphism γ between R[x]/<xN−λ> and a direct sum ⊕b∈IS(rb) of certain local rings, where I is the complete set of representatives of p-cyclotomic cosets modulo n1. By this isomorphism, all codes over R and their dual codes are obtained from the ideals of S(rb). In addition, we determine explicitly the inverse of γ so that the unique polynomial representations of λ-constacyclic codes may be calculated. Finally, for k=2 the exact number of such codes is provided.

Symbol-Pair Distances of Repeated-Root Negacyclic Codes of Length 2s over Galois Rings

Negacyclic codes of length [Formula: see text] over the Galois ring [Formula: see text] are linearly ordered under set-theoretic inclusion, i.e., they are the ideals [Formula: see text], [Formula: see text], of the chain ring [Formula: see text]. This structure is used to obtain the symbol-pair distances of all such negacyclic codes. Among others, for the special case when the alphabet is the finite field [Formula: see text] (i.e., [Formula: see text]), the symbol-pair distance distribution of constacyclic codes over [Formula: see text] verifies the Singleton bound for such symbol-pair codes, and provides all maximum distance separable symbol-pair constacyclic codes of length [Formula: see text] over [Formula: see text].

Symbol-Pair Distance of Repeated-Root Constacyclic Codes of Prime Power Lengths over \({{\mathbb{F}_{p^m}[u]}/{\langle u^3\rangle}}\)

Let p be a prime, s, m be positive integers, γ be a nonzero element of the finite field Fpm, and let R=Fpm[u]/⟨u3⟩ be the finite commutative chain ring. In this paper, the symbol-pair distances of all γ-constacyclic codes of length ps over R are completely determined.

New Quantum and LCD Codes over Finite Fields of Even Characteristic

For an integer m ≥ 1, we study cyclic codes of length l over a commutative non-chain ring F2m + uF2m , where u2 = u . With a new Gray map and Euclidean dual-containing cyclic codes, we provide many new and superior codes to the best-known quantum error-correcting codes. Also, we characterise LCD codes of length l with respect to their generator polynomials and prove that F2m − image of an LCD code of length l is an LCD code of length 2l . Finally, we provide several optimal LCD codes from the Gray images of LCD codes over F2m + uF2m .

Quantum Codes Obtained through Constacyclic Codes over Z3 + νZ3 + ωZ3 + νωZ3

This paper is concerned with, structural properties and construction of quantum codes over Z3 by using constacyclic codes over the finite commutative non-chain ring R = Z3 + νZ3 + ωZ3 + νωZ3 where ν2 = 1, ω2 = ω, νω = νω, and Z3 is field having 3 elements with characteristic 3. A Gray map is defined between R and Z43. The parameters of quantum codes over Z3 are obtained by decomposing constacyclic codes into cyclic and negacyclic codes over Z3. As an application, some examples of quantum codes of arbitrary length, are also obtained.