Results 241 to 250 of about 3,045,703 (258)

Quantum codes over a class of finite chain ring

Quantum Information and Computation, 2016
In this study, we introduce a new Gray map which preserves the orthogonality from the chain ring F_2 [u] / (u^s ) to F^s_2 where F_2 is the finite field with two elements. We also give a condition of the existence for cyclic codes of odd length containing its dual over the ring F_2 [u] / (u^s ) .
Siap, Irfan, Sarı, Mustafa
openaire   +3 more sources

Properties of finite unrefinable chains of ring topologies

Journal of Mathematical Sciences, 2012
Rings are not necessarily associative, topological spaces not necessarily Hausdorff. It is known that the set of all ring topologies on a ring \(R\) forms a lattice. The author studies the following question related to the Schmidt-Ore theorem about principal series in modular lattices: Let \(R\) be a ring, \(\mathfrak M\) a lattice of ring topologies ...
openaire   +2 more sources

Finite maximal chains of commutative rings

Journal of Algebra and Its Applications, 2014
Let R ⊆ S be a unital extension of commutative rings, with [Formula: see text] the integral closure of R in S, such that there exists a finite maximal chain of rings from R to S. Then S is a P-extension of R, [Formula: see text] is a normal pair, each intermediate ring of R ⊆ S has only finitely many prime ideals that lie over any given prime ideal of
Ayache, Ahmed, Dobbs, David E.
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$$\sigma $$-LCD codes over finite chain rings

Designs, Codes and Cryptography, 2019
In this paper, the authors studied the $\sigma$-LCD codes over finite chain rings. They characterize $\sigma$-LCD linear codes over finite chain rings by using their generator matrix. A necessary and sufficient condition for a linear code to be $\sigma$-LCD over a series of finite chain rings is given.
Liu, Xiusheng, Liu, Hualu
openaire   +2 more sources

On the Structure of Linear and Cyclic Codes over a Finite Chain Ring

Applicable Algebra in Engineering, Communication and Computing, 2000
In [\textit{A. R. Calderbank} and \textit{N. J. A. Sloane}, Des. Codes Cryptography 6, 21-35 (1995; Zbl 0848.94020)], structure theorems are given for linear and cyclic codes over \(\mathbb{Z}_{p^a}\). Such codes received much attention after the discovery that important families of binary nonlinear codes can be obtained as images under a Gray mapping ...
Graham H. Norton, Ana Salagean
openaire   +2 more sources

Non-isomorphic pure finite chain rings

Afrika Matematika, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tabue, Alexandre Fotue, Mouaha, Christophe   +1 more
openaire   +1 more source

Finite chain rings

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 1973
Clark, W. Edwin, Drake, David A.
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Properties of finite unrefinable chains of ring topologies for nilpotent rings

2018
Below \(\mathfrak M\) denotes the lattice of all ring topologies on a ring \(R\) and \(\mathfrak N\) the sublattice of \(\mathfrak M\) of ring topologies having a fundamental system of neighborhoods of zero consisting of subgroups of the additive group \(R(+)\) of \(R\). It is said that an element \(b\) of a lattice \((\mathfrak L,
Arnautov, V. I., Ermakova, G. N.
openaire   +1 more source

The depth spectrums of constacyclic codes over finite chain rings

Discrete Mathematics, 2015
Hongjuan Ma, Xiying Zheng
exaly  

Linear and cyclic codes over direct product of finite chain rings

Mathematical Methods in the Applied Sciences, 2018
Roger Ten-Valls, Cristina Fernández-Córdoba   +1 more
exaly