Results 21 to 30 of about 3,398,533 (269)
Density of free modules over finite chain rings
Linear Algebra and its Applications, 2022 In this paper we focus on modules over a finite chain ring $\mathcal{R}$ of size $q^s$. We compute the density of free modules of $\mathcal{R}^n$, where we separately treat the asymptotics in $n,q$ and $s$. In particular, we focus on two cases: one where we fix the length of the module and one where we fix the rank of the module.
Eimear Byrne +3 more
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Mathematics, 2021 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.
Mohammed E. Charkani +3 more
doaj +1 more source
Constacyclic codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020 The family of finite local Frobenius non-chain rings of length 5 and nilpotency index 4 is determined, as a by-product all finite local Frobenius non-chain rings with p5 elements (p a prime) and nilpotency index 4 are given.
Castillo-Guillén C. A. +1 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 $Γ(\texttt{R})$ the Teichmüller'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 ...
Alexandre Fotue Tabue, Christophe Mouaha
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, 2002 Over the past 25 years, I have been immersed in research in Algebra and more particularly in ring theory. I embarked on writing this book on Smarandache rings (Srings) specially to motivate both ring theorists and Smarandache algebraists to develop and ...
Vasantha, Kandasamy
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On Multiplicative Matrix Channels over Finite Chain Rings [PDF]
Journal of Communication and Information Systems, 2013 23 pages, 4 ...
Roberto Wanderley da Nóbrega +3 more
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The invariant rings of the Sylow groups of GU(3,q2), GU(4,q2), Sp(4,q) and O+(4,q) in the natural characteristic [PDF]
, 2016 Let G be a Sylow p -subgroup of the unitary groups GU(3,q2)GU(3,q2), GU(4,q2)GU(4,q2), the symplectic group Sp(4,q)Sp(4,q) and, for q odd, the orthogonal group O+(4,q)O+(4,q).
Fleischmann, Peter +2 more
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Hamming Distance of Constacyclic Codes of Length
IEEE Access, 2021 Let $p$ be any prime, $s$ and $m$ be positive integers. In this paper, we completely determine the Hamming distance of all constacyclic codes of length $p^s$ over the finite commutative chain ring $\mathbb {F}_{p^m}+ u\mathbb {F}_{p^m} + u^{2 ...
Hai Q. Dinh +3 more
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Some conditions for finiteness of a ring
International Journal of Mathematics and Mathematical Sciences, 1988 Extending a result of Putcha and Yaqub, we prove that a non-nil ring must be finite if it has both ascending chain condition and descending chain condition on non-nil subrings.
Howard E. Bell
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On Hamming Distance Distributions of Repeated-Root Cyclic Codes of Length 5ps Over Fp m + uFp m
IEEE Access, 2022 Let $p\not =5$ be any odd prime. Using the algebraic structures of all cyclic codes of length $5p^{s}$ over the finite commutative chain ring ${\mathcal{ R}}=\mathbb F_{p^{m}}+u\mathbb F_{p^{m}}$ , in this paper, the exact values of Hamming ...
Hai Q. Dinh +3 more
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