Results 11 to 20 of about 68 (66)

Generalized weights of codes over rings and invariants of monomial ideals [PDF]

, 2023
We develop an algebraic theory of supports for \(R\)-linear codes of fixed length, where \(R\) is a finite commutative unitary ring. A support naturally induces a notion of generalized weights and allows one to associate a monomial ideal to a code.
Ravagnani, Alberto, Gorla, Elisa
core   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

A catalogue of three-level regular fractional factorial designs

, 2005
Clear effect, Linear code, Minimum aberration, Moment aberration, Resolution, 62K15, 94B05,
Hongquan Xu
core   +1 more source

Representability of the direct sum of uniform \(q\)-matroids [PDF]

There are many similarities between the theories of matroids and \(q\)-matroids. However, when dealing with the direct sum of \(q\)-matroids many differences arise.
Zullo, Ferdinando, Alfarano, Gianira N., Jurrius, Relinde, Neri, Alessandro   +3 more
core   +1 more source

Complete caps in projective spaces PG(n, [PDF]

, 2004
. A computer search in the finite projective spaces PG(n, q) for the spectrum of possible sizes k of complete k-caps is done. Randomized greedy algorithms are applied. New upper bounds on the smallest size of a complete cap are given for many values of n
Fernanda Pambianco, Stefano Marcugini, Alexander A Davydov   +2 more
core  

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
doaj   +1 more source

Kneser-Hecke-operators in coding theory

, 2006
The Kneser-Hecke-operator is a linear operator defined on the complex vector space spanned by the equivalence classes of a family of self-dual codes of fixed length.
Gabriele Nebe, Nebe, Gabriele
core   +1 more source

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
doaj   +1 more source