Results 31 to 40 of about 226,788 (288)
On skew cyclic codes over $ M_{2}(\mathbb{F}_{2}) $
AIMS Mathematics, 2023 The algebraic structure of skew cyclic codes over $ M_{2} $($ \mathbb{F}_2 $), using the $ \mathbb{F}_4 $-cyclic algebra, is studied in this work. We determine that a skew cyclic code with a polynomial of minimum degree $ d(x) $ is a free code generated ...
Xuesong Si, Chuanze Niu
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Lifted codes and lattices from codes over finite chain rings [PDF]
Cryptography and Communications, 2020 In this paper we give the generalization of lifted codes over any finite chain ring. This has been done by using the construction of finite chain rings from p-adic fields.
Reguia Lamia Bouzara +2 more
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 Over finite local Frobenius non-chain rings of length 5 and nilpotency index 4 and when the length of the code is relatively prime to the characteristic of the residue field of the ring, the structure of the dual of γ-constacyclic codes is established ...
Castillo-Guillén C. A. +1 more
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Carbon Trends, 2022 The quasi-particle (QP) bands of polyacene (PAC) – an infinite linear chain of fused benzene rings – are reconstructed from the QP spectra of oligoacenes (OACs) with N∈[5,30] (N is the number of fused rings) obtained using a computational methodology ...
Anna Pomogaeva +2 more
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LIFTED CODES OVER FINITE CHAIN RINGS [PDF]
, 2011 In this paper, we study lifted codes over finite chain rings.
Dougherty, Steven T. +2 more
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Skew constacyclic codes over finite chain rings
Advances in Mathematics of Communications, 2012 Skew polynomial rings over finite fields ([7] and [10]) and over Galois rings ([8]) have been used to study codes. In this paper, we extend this concept to finite chain rings. Properties of skew constacyclic codes generated by monic right divisors of $x^n- $, where $ $ is a unit element, are exhibited.
Jitman, Somphong +2 more
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Contraction of cyclic codes over finite chain rings [PDF]
Discrete Mathematics, 2018 Let $\texttt{R}$ be a commutative finite chain ring of invariants $(q,s)$ and $ (\texttt{R})$ the Teichm ller's set of $\texttt{R}.$ In this paper, the trace representation cyclic $\texttt{R}$-linear codes of length $\ell,$ is presented, when $\texttt{gcd}(\ell, q) = 1.$ We will show that the contractions of some cyclic $\texttt{R}$-linear codes of ...
Fotue Tabue, Alexandre +1 more
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Expanders on matrices over a finite chain ring, I
International Journal of Mathematics, 2023 In this work and its sequel, we study the expanding phenomenon of matrices over a finite chain ring of large residue field. A sum-product estimate is proved. It is shown that [Formula: see text] is a moderate expander on [Formula: see text] matrices with exponent [Formula: see text].
Dung M. Ha, Hieu T. Ngo
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New quantum codes from constacyclic codes over finite chain rings [PDF]
Quantum Information ProcessingLet R be the finite chain ring Fp2m+uFp2m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt ...
Yongsheng Tang +3 more
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Dimensional groups and fields [PDF]
, 2019 We shall define a general notion of dimension, and study groups and rings whose interpretable sets carry such a dimensio. In particular, we deduce chain conditions for groups, definability results for fields and domains, and show that pseudofinite groups
Wagner, Frank Olaf
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