Results 11 to 20 of about 51 (51)

A Family Of Low Density Matrices In Lagrangian–Grassmannian

Special Matrices, 2018
The aim of this paper is twofold. First, we show a connection between the Lagrangian- Grassmannian variety geometry defined over a finite field with q elements and the q-ary Low-Density Parity- Check codes. Second, considering the Lagrangian-Grassmannian
Carrillo-Pacheco Jesús, Jarquín-Zárate Fausto   +1 more
doaj   +1 more source

DAGS: Key encapsulation using dyadic GS codes

Journal of Mathematical Cryptology, 2018
Code-based cryptography is one of the main areas of interest for NIST’s Post-Quantum Cryptography Standardization call. In this paper, we introduce DAGS, a Key Encapsulation Mechanism (KEM) based on quasi-dyadic generalized Srivastava codes.
Banegas Gustavo, Barreto Paulo S. L. M., Boidje Brice Odilon, Cayrel Pierre-Louis, Dione Gilbert Ndollane, Gaj Kris, Gueye Cheikh Thiécoumba, Haeussler Richard, Klamti Jean Belo, N’diaye Ousmane, Nguyen Duc Tri, Persichetti Edoardo, Ricardini Jefferson E.   +12 more
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Codes Over Hyperfields

Discussiones Mathematicae - General Algebra and Applications, 2017
In this paper, we define linear codes and cyclic codes over a finite Krasner hyperfield and we characterize these codes by their generator matrices and parity check matrices.
Atamewoue Surdive, Ndjeya Selestin, Strüngmann Lutz, Lele Celestin   +3 more
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The study of ℤpℤp[u, v]-additive cyclic codes and their application in obtaining Optimal and MDSS codes

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica
Let S = ℤp[u, v]/〈u2, v2, uv − uv〉 be a semi-local ring, where p is a prime number. In the present article, we determine the generating sets of S and use them to construct the structures of ℤpS-additive cyclic and constacyclic codes.
Ashraf Mohammad, Asim Mohd, Mohammad Ghulam, Rehman Washiqur   +3 more
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Constacyclic codes over 𝔽q𝒮𝒯 and their applications

AKCE International Journal of Graphs and Combinatorics
Let [Formula: see text], where p is an odd prime and r is a positive integer. Consider a ring [Formula: see text], where [Formula: see text] with [Formula: see text] and [Formula: see text] with [Formula: see text].
Amal S. Alali, Mohd Azmi, Nadeem ur Rehman, Mohammad Fareed Ahmad   +3 more
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Vanishing Ideals Over Odd Cycles

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019
Let K be a finite field. Let X* be a subset of the a ne space Kn, which is parameterized by odd cycles. In this paper we give an explicit Gröbner basis for the vanishing ideal, I(X*), of X*.
Uribe-Paczka M. Eduardo, Sarmiento Eliseo, Márquez Carlos Rentería   +2 more
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Linear Skew Cyclic Codes over 𝔽qS

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica
In this study, we focus on skew cyclic codes over the family of rings 𝔽q S where q is a power of a prime number and S = 𝔽q + v𝔽q with v2 = v. Structural properties of these codes are studied in detail. Obtained results lead us to characterize 𝔽q S-linear
Yildirim Tulay
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On reversibility problem in DNA bases over a class of rings

Applied Mathematics in Science and Engineering
Let [Formula: see text] be a non-chain ring of characteristic 4, where [Formula: see text] and [Formula: see text]. In this article, we discuss reversible cyclic codes of odd lengths over the ring [Formula: see text].
Amal S. Alali, Mohammad Ashraf, Washiqur Rehman, Ghulam Mohammad, Mohd Asim   +4 more
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Skew cyclic codes over 𝔻4R and their applications to DNA codes construction

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica
The fundamental aim of this research is to analyze the configuration of 𝔽4R submodules, skew cyclic codes over 𝔽4R and establish their connection with DNA codes, where 𝔽4 is a field of order 4 and R = 𝔽4 + u𝔽4 + v𝔽4 + w𝔽4 with u2 = u, v2 = v, w2 = w, uv =
Rehman Nadeem ur, Ahmad Mohammad Fareed, Azmi Mohd   +2 more
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Two-dimensional cyclic codes over a finite chain ring

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica
In 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   +1 more source