On the Hamming distances of repeated-root constacyclic codes of length 4ps

Let $p$ be an odd prime, $s$, $m$ be positive integers, $\gamma ,\lambda$ be nonzero elements of the finite field ${\mathbb{F}}_{p^m}$ such that ${\gamma }^{p^s}=\lambda$. In this paper, we show that, for any positive integer $\eta$, the Hamming distances of all repeated-root $\lambda$-constacyclic codes of length $\eta p^s$ can be determined by those of certain simple-root $\gamma$-constacyclic codes of length $\eta$. Using this result, Hamming distances of all constacyclic codes of length $4p^s$ are obtained. As an application, we identify all MDS $\lambda$-constacyclic codes of length $4p^s$.     

The dual code of any (δ+αu2)-constacyclic code over F2m[u]∕〈u4〉 of oddly even length

Let ${\mathbb{F}}_{2^m}$ be a finite field of cardinality $2^m$, $R={\mathbb{F}}_{2^m}\left[u\right]∕〈u^4〉={\mathbb{F}}_{2^m}+u{\mathbb{F}}_{2^m}+u^2{\mathbb{F}}_{2^m}+u^3{\mathbb{F}}_{2^m}$ $(u^4=0)$ which is a finite chain ring, and $n$ is an odd positive integer. For any $\delta ,\alpha \in {\mathbb{F}}_{2^m}^{\times }$, an explicit representation for the dual code of any $(\delta +\alpha u^2)$-constacyclic code over $R$ of length $2n$ is given. And some dual codes of $(1+u^2)$-constacyclic codes over $R$ of length 14 are constructed. For the case of $\delta =1$, all distinct self-dual $(1+\alpha u^2)$-constacyclic codes over $R$ of length $2n$ are determined.     

1-(2′,2′,2′-Trifluoroethyl)-4-phosphopyrazoles: Synthese et Etude Spectroscopique ir et RMN 1H, 13C, 19F,et 31P

Seven new 1-fluorinated-4-phosphopyrazoles 2 have been prepared in 60–94% yield by cyclization of N-(2′,2′,2′-trifluoroethyl) phosphonyl β-hydrazones 1 with triethyl orthoformate in the presence of acetic acid. The IR data, the ¹H, ¹³C, ¹⁹F, ³¹P chemical shifts and coupling constants of the compounds 2 are reported.     

SYNTHESIS OF SOME SULFUR-CONTAINING SPIROINDOLE DERIVATIVES

Abstract

The synthesis of some new sulfur-containing spiroindole derivatives is reported. Fluorinated 3′-aryl-2′-phenylimino-spiro[3H-indole-3,6′[4,5′-pyrazolin][4,3-d]thiazolo]2(1H)-ones were prepared by the reaction of 5-(2-oxo-3-indolinylidene)-3-aryl-2-phenylimino-4-thiazolidinones with hydrazine hydrate. The compounds have been characterized on the basis of elemental and spectral studies.     

Flexizyme‐Mediated Genetic Reprogramming As a Tool for Noncanonical Peptide Synthesis and Drug Discovery

Noncanonical peptides occur frequently in Nature, and often display high bioactivity. However, the lack of tractable systems for the synthesis of diverse libraries of such peptides has thus far hampered their development as drugs. Genetic reprogramming techniques, in which noncanonical amino acids may be incorporated into peptides, have largely removed this limitation. This Concept article outlines the development of these techniques with an emphasis on drug discovery.