Results 11 to 20 of about 3,398,533 (269)
Two-dimensional cyclic codes over a finite chain ring
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria MatematicaIn this paper, we have determined the generators and rank of a 2D cyclic code of length mn over a finite chain ring ℛ with residue field 𝔽q, where m is arbitrary and q ≡ 1(mod n).
Garg Disha, Dutt Sucheta
doaj +2 more sources
Reversible cyclic codes over finite chain rings [PDF]
CoRR, 2023 In this paper, necessary and sufficient conditions for the reversibility of a cyclic code of arbitrary length over a finite commutative chain ring have been derived. MDS reversible cyclic codes having length p^s over a finite chain ring with nilpotency index 2 have been characterized and a few examples of MDS reversible cyclic codes have been presented.
Monika Dalal +2 more
core +5 more sources
, 1970 The theory of near-rings has arisen in a variety of ways. There is a natural desire to generalise the theory of rings and skew fields by relaxing some of their defining axioms.
Holcombe, William Michael Lloyd
core +7 more sources
On LCD, self dual and isodual cyclic codes over finite chain rings [PDF]
, 2022 Altres ajuts: acords transformatius de la UABIn this paper, LCD cyclic, self dual and isodual codes over finite chain rings are investigated. It was proven recently that a non-free LCD cyclic code does not exist over finite chain rings.
Fernández Córdoba, Cristina +2 more
core +1 more source
On the Density of Codes over Finite Chain Rings
2023 IEEE Information Theory Workshop (ITW), 2023 We determine the asymptotic proportion of free modules over finite chain rings with good distance properties and treat the asymptotics in the code length n and the residue field size q separately. We then specialize and apply our technique to rank metric codes and to Hamming metric codes.
Anna-Lena Horlemann +2 more
openaire +4 more sources
DNA codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022 A one to one correspondence between the elements of a finite local Frobenius non-chain ring of length 5 and nilpotency index 4, and k-tuples of DNA codewords is established.
Castillo-Guillén C. A. +1 more
doaj +1 more source
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
openaire +4 more sources
Algebraic Methods for Finite Linear Cellular Automata [PDF]
, 1996 PhDCellular automata are a simple class of extended dynamical systems which have been much studied in recent years. Linear cellular automata are the class of cellular automata most amenable to algebraic analytic treatments, algebraic techniques are ...
Dow, R. A.
core +4 more sources
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
doaj +1 more source
Symbol-Triple Distance of Repeated-Root Constacyclic Codes of Prime Power Lengths over
Mathematics, 2022 Let p be an odd prime, where ϑ and m are positive integers. Let ψ be a nonzero element of the finite field Fq, where q=pm, and R=Fq+uFq+u2Fq(u3=0). In this paper, we determine completely the symbol-triple distances of all ψ-constacyclic codes of length ...
Hai Q. Dinh +3 more
doaj +1 more source