Results 21 to 30 of about 12,890,521 (357)

Construction of MDS Self-dual Codes over Finite Fields [PDF]

Finite Fields Their Appl., 2018
In this paper, we obtain some new results on the existence of MDS self-dual codes utilizing (extended) generalized Reed-Solomon codes over finite fields of odd characteristic.
Khawla Labad, Hongwei Liu, Jinquan Luo
semanticscholar   +1 more source

On Inverses of Permutation Polynomials of Small Degree Over Finite Fields [PDF]

IEEE Transactions on Information Theory, 2018
Permutation polynomials (PPs) and their inverses have applications in cryptography, coding theory and combinatorial design theory. In this paper, we make a brief summary of the inverses of PPs of finite fields, and give the inverses of all PPs of degree ≤
Yanbin Zheng, Qiang Wang, Wenhong Wei
semanticscholar   +1 more source

Some Multisecret-Sharing Schemes over Finite Fields

Mathematics, 2020
A secret sharing scheme is a method of assigning shares for a secret to some participants such that only some distinguished subsets of these subsets can recover the secret while other subsets cannot.
Selda Çalkavur, Patrick Solé
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Constructions of optimal LCD codes over large finite fields [PDF]

Finite Fields Their Appl., 2017
In this paper 1 , we prove existence of optimal complementary dual codes (LCD codes) over large finite fields. We also give methods to generate orthogonal matrices over finite fields and then apply them to construct LCD codes.
Lin Sok, Minjia Shi, P. Solé
semanticscholar   +1 more source

THEORETICAL ASSUMPTIONS FOR AN INTRODUCTION TO ELLIPTIC CURVE CRYPTOGRAPHY

STED Journal, 2023
Understanding elliptic curves contributed to solving mathematical problems in number theory that had been unsolved for centuries. Elliptic curves were also used in solving one of the millennial problems, which is Fermat's last theorem.
Ognjen Milivojević, Boris Damjanović
doaj   +1 more source

Chebyshev Action on Finite Fields [PDF]

, 2013
Given a polynomial f and a finite field F one can construct a directed graph where the vertices are the values in the finite field, and emanating from each vertex is an edge joining the vertex to its image under f.
Gassert, T. Alden
core   +1 more source

A note on permutation polynomials over finite fields [PDF]

Finite Fields Their Appl., 2017
Permutation polynomials over finite fields constitute an active research area and have applications in many areas of science and engineering. In this paper, two conjectures on permutation polynomials proposed recently by Wu and Li [19] are settled ...
Jingxue Ma, G. Ge
semanticscholar   +1 more source

Associative nil-algebras over finite fields [PDF]

, 2013
The nilpotency degree of a relatively free finitely generated associative algebra with the identity $x^n=0$ is studied over finite fields.Comment: 12 ...
Artem A. Lopatin, Ivan, P. Shestakov
core   +1 more source

Subspace Codes Based on Partial Injective Maps of Vector Spaces Over Finite Fields

IEEE Access, 2020
Subspace codes are widely used in error corrections of random network coding. In this article, subspace codes based on partial injective maps of vector spaces over finite fields are considered. Several bounds of the subspace codes (n, M, 2b, e)q based on
Hong-Li Wang, Gang Wang, You Gao
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LCD Cyclic Codes Over Finite Fields [PDF]

IEEE Transactions on Information Theory, 2016
In addition to their applications in data storage, communications systems, and consumer electronics, linear complementary dual (LCD) codes—a class of linear codes—have been employed in cryptography recently.
Chengju Li, C. Ding, Shuxing Li
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