Results 21 to 30 of about 10,130,538 (248)
, 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
core +1 more source
On Group Codes Over Elementary Abelian Groups
Sultan Qaboos University Journal for Science, 2003 For group codes over elementary Abelian groups we present definitions of the generator and the parity check matrices, which are matrices over the ring of endomorphism of the group.
Adnan A. Zain
doaj +1 more source
Decoding Linear Codes over Chain Rings Given by Parity Check Matrices
Mathematics, 2021 We design a decoding algorithm for linear codes over finite chain rings given by their parity check matrices. It is assumed that decoding algorithms over the residue field are known at each degree of the adic decomposition.
José Gómez-Torrecillas +2 more
doaj +1 more source
Demi-matroids from codes over finite Frobenius rings
, 2015 We present a construction of demi-matroids, a generalization of matroids, from linear codes over finite Frobenius rings, as well as a Greene-type identity for rank generating functions of demi-matroids.
Westerbäck, Thomas, +4 more
core +1 more source
Classification of Certain Cyclic LCD Codes
Scientific Annals of Computer ScienceWe show that a necessary and sufficient condition for a cyclic code C of length N over a finite chain ring R (whose maximal ideal has nilpotence 2) to be an LCD code is that C = (f(x)), where f(X) is a self-reciprocal monic divisor of X^N − 1 in R[X] and
Seth Gannon, Hamid Kulosman
doaj +1 more source
The Gilbert-Varshamov Bound for Stabilizer Codes Over
IEEE Access, 2018 Quantum codes over finite rings have received a great deal of attention in recent years. Compared with quantum codes over finite fields, a notable advantage of quantum codes over finite rings is that they can adapt to quantum physical systems of ...
Nianqi Tang +3 more
doaj +1 more source
Mathematics, 2023 Let k,m be positive integers and F2m be a finite field of order 2m of characteristic 2. The primary goal of this paper is to study the structural properties of cyclic codes over the ring Sk=F2m[v1,v2,…,vk]⟨vi2−αivi,vivj−vjvi⟩, for i,j=1,2,3,…,k, where αi
Shakir Ali +3 more
doaj +1 more source
Construction of MDS self-dual codes over Galois rings
, 2017 The purpose of this paper is to construct nontrivial MDS self-dual codes over Galois rings. We consider a building-up construction of self-dual codes over Galois rings as a GF(q)-analogue of (Kim and Lee, J Combin Theory ser A, 105:79-95).
이윤진
core +1 more source
Formal Groups and Hopf Algebras over Discrete Rings [PDF]
, 1974 A theory of formal schemes and groups over abitrary rings is presented. The flat formal schemes in this theory have coalgebras of distributions which behave in the usual way. Frobenius and Verschiebung maps are studied.
Robert A. Morris +3 more
core +1 more source
Network Communication with operators in Dedekind Finite and Stably Finite Rings [PDF]
, 2016 Messages in communication networks often are considered as "discrete" taking values in some finite alphabet (e.g. a finite field). However, if we want to consider for example communication based on analogue signals, we will have to consider messages that
Riis, S
core +4 more sources