Results 41 to 50 of about 176,479 (165)

Ranked solutions of the matric equation A1X1=A2X2

International Journal of Mathematics and Mathematical Sciences, 1980
Let GF(pz) denote the finite field of pz elements. Let A1 be s×m of rank r1 and A2 be s×n of rank r2 with elements from GF(pz). In this paper, formulas are given for finding the number of X1,X2 over GF(pz) which satisfy the matric equation A1X1=A2X2 ...
A. Duane Porter, Nick Mousouris
doaj   +1 more source

Optimal quinary cyclic codes with minimum distance four

Tongxin xuebao, 2017
Cyclic codes are an extremely important subclass of linear codes.They are widely used in the communication systems and data storage systems because they have efficient encoding and decoding algorithm.Until now,how to construct the optimal ternary cyclic ...
Ye TIAN, Yu-qing ZHANG, Yu-pu HU
doaj  

Reversible Self-Dual Codes over Finite Field

Cauchy: Jurnal Matematika Murni dan Aplikasi
Reversible self-dual code is a linear code which combine the properties from self-dual code and reversible code. Previous research shows that reversible self-dual codes have only been developed over field of order 2 and order 4.
Ardi Nur Hidayat, Vira Hari Krisnawati, Abdul Rouf Alghofari   +2 more
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Elements of high order in Artin-Shreier extensions of finite fields(in Ukrainian) [PDF]

Математичні Студії, 2013
We construct explicitly in any finite field of the form $F_{p^p}$ elements with multiplicative order larger than $4^p$.
R. B. Popovych
doaj  

On fundamental sets over a finite field

International Journal of Mathematics and Mathematical Sciences, 1985
A partition over finite field is defined and each equivalence class is constructed and represented by a set called the fundamental set. If a primitive element is used to construct the addition table over these fundamental sets then all additions over the
Yousef Abbas, Joseph J. Liang
doaj   +1 more source

On Matrix Representation of Extension Field GF(p^L) and Its Application in Vector Linear Network Coding

Entropy
For a finite field GF(pL) with prime p and L>1, one of the standard representations is L×L matrices over GF(p) so that the arithmetic of GF(pL) can be realized by the arithmetic among these matrices over GF(p). Based on the matrix representation of GF(pL)
Hanqi Tang, Heping Liu, Sheng Jin, Wenli Liu, Qifu Sun   +4 more
doaj   +1 more source

Point Compression and Coordinate Recovery for Edwards Curves over Finite Field

Annals of the West University of Timisoara: Mathematics and Computer Science, 2014
We present two computational approaches for the purpose of point compression and decompression on Edwards curves over the finite field Fp where p is an odd prime.
Justus Benjamin
doaj   +1 more source

Chebyshev action on finite fields

Discrete Mathematics, 2014
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. When f is a Chebyshev polynomial of prime degree, the graphs display an unusual degree of symmetry.
openaire   +2 more sources

Finite Fields and Ramanujan Graphs

Journal of Combinatorial Theory, Series B, 1997
A connected \(k\)-regular graph is called a Ramanujan graph if the modulus of any eigenvalue (of its adjacency matrix), different from \(\pm k\), does not exceed \(2\sqrt{k-1}\). The author gives a new method to construct Ramanujan graphs, and he constructs two new families of Ramanujan graphs.
openaire   +1 more source

An adaptive cryptosystem on a Finite Field. [PDF]

PeerJ Comput Sci, 2021
Bhowmik A, Menon U.
europepmc   +1 more source