Results 11 to 20 of about 11,891,302 (357)
Faster polynomial multiplication over finite fields [PDF]
Journal of the ACM, 2014 Let p be a prime, and let M_p(n) denote the bit complexity of multiplying two polynomials in F_p[X] of degree less than n. For n large compared to p, we establish the bound M_p(n) = O(n log n 8^(log^* n) log p), where log^* is the iterated logarithm ...
Harvey, David +2 more
core +4 more sources
FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs [PDF]
Journal of High Energy Physics, 2019 A bstractComplex algebraic calculations can be performed by reconstructing analytic results from numerical evaluations over finite fields. We describe FiniteFlow, a framework for defining and executing numerical algorithms over finite fields and ...
T. Peraro
semanticscholar +1 more source
Entanglement-assisted quantum error-correcting codes over arbitrary finite fields [PDF]
Quantum Information Processing, 2018 We prove that the known formulae for computing the optimal number of maximally entangled pairs required for entanglement-assisted quantum error-correcting codes (EAQECCs) over the binary field hold for codes over arbitrary finite fields as well.
C. Galindo +3 more
semanticscholar +1 more source
On Two-to-One Mappings Over Finite Fields [PDF]
IEEE Transactions on Information Theory, 2019 Two-to-one (2-to-1) mappings over finite fields play an important role in symmetric cryptography. In particular they allow to design APN functions, bent functions and semi-bent functions. In this paper we provide a systematic study of two-to-one mappings
Sihem Mesnager, Longjiang Qu
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
Constructions of Involutions Over Finite Fields [PDF]
IEEE Transactions on Information Theory, 2018 An involution over finite fields is a permutation polynomial whose inverse is itself. Owing to this property, involutions over finite fields have been widely used in applications, such as cryptography and coding theory.
Dabin Zheng +4 more
semanticscholar +1 more source
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
semanticscholar +1 more source
Scattering amplitudes over finite fields and multivariate functional reconstruction [PDF]
, 2016 A bstractSeveral problems in computer algebra can be efficiently solved by reducing them to calculations over finite fields. In this paper, we describe an algorithm for the reconstruction of multivariate polynomials and rational functions from their ...
T. Peraro
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
New Construction of Low-Density Parity-Check Codes Based on Vector Space Over Finite Fields
IEEE Access, 2020 Low-Density Parity-Check (LDPC) codes have low linear decoding complexity, which is a kind of good codes with excellent performance. Therefore, LDPC codes have great research value.
Xuemei Liu, Lihua Jia
doaj +1 more source