Download or read book Counting Polynomial Matrices over Finite Fields written by Julia Lieb and published by BoD – Books on Demand. This book was released on 2017-09-15 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dealing with three mathematical areas, namely polynomial matrices over finite fields, linear systems and coding theory. Primeness properties of polynomial matrices provide criteria for the reachability and observability of interconnected linear systems. Since time-discrete linear systems over finite fields and convolutional codes are basically the same objects, these results could be transferred to criteria for non-catastrophicity of convolutional codes. In particular, formulas for the number of pairwise coprime polynomials and for the number of mutually left coprime polynomial matrices are calculated. This leads to the probability that a parallel connected linear system is reachable and that a parallel connected convolutional code is non-catastrophic. Moreover, other networks of linear systems and convolutional codes are considered.

Download or read book A Note on Polynomial Matrix Functions Over a Finite Field written by J. V. Brawley and published by . This book was released on 1977 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let F = GF(q) denote the finite field of order q, and let F(n) denote the ring of n x n matrices over F. This paper obtains a unique representation for and determines the number of right (left) polynomial functions A:F(n) yields F(n).

Download or read book Counting Zeros of Polynomials Over Finite Fields written by Daniel Edwin Erickson and published by . This book was released on 1974 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Scalar Polynomial Functions on the Nxn Matrices Over a Finite Field written by Joel Vincent Brawley and published by . This book was released on 1973 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of the theory of finite fields in areas of discrete linear modeling such as coding theory, finite linear sequential machines, algebraic cryptography and the construction of block designs is well-known. Many times one has the task of constructing (based on a finite field) a function having certain prescribed properties. Of such a nature is the material contained in the report. In particular, the authors determined among other things, necessary and sufficient conditions on a polynomial f(x) with coefficients in a finite field F in order that it defines via substitution a one-one onto function (a permutation) from F(nxn), the nxn matrices over F, to F(nxn).

Download or read book Error Free Polynomial Matrix Computations written by E.V. Krishnamurthy and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is written as an introduction to polynomial matrix computa tions. It is a companion volume to an earlier book on Methods and Applications of Error-Free Computation by R. T. Gregory and myself, published by Springer-Verlag, New York, 1984. This book is intended for seniors and graduate students in computer and system sciences, and mathematics, and for researchers in the fields of computer science, numerical analysis, systems theory, and computer algebra. Chapter I introduces the basic concepts of abstract algebra, including power series and polynomials. This chapter is essentially meant for bridging the gap between the abstract algebra and polynomial matrix computations. Chapter II is concerned with the evaluation and interpolation of polynomials. The use of these techniques for exact inversion of poly nomial matrices is explained in the light of currently available error-free computation methods. In Chapter III, the principles and practice of Fourier evaluation and interpolation are described. In particular, the application of error-free discrete Fourier transforms for polynomial matrix computations is consi dered.

Download or read book Finite Fields and their Applications written by James A. Davis and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-10-26 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

Download or read book The Number of Polynomial Functions Which Permute the Matrices Over a Finite Field written by Joel V Brawley (Jr) and published by . This book was released on 1974 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let F denote a finite field and let f sub (n x n) denote the n x n matrices over F.A function f:F sub (n x n) maps to F sub (n x n) is called a (scalar) polynomial function on F sub (n x n) if and only if there exists a polynomial f(x) an element of F(in brackets:(x)) which represents f under substitution. A formula is obtained for the number of polynomial function on F sub (n x n) which are permutations of F sub (n x n). In the process a procedure is outlined for obtaining a unique polynomial representations of each permutation polynomial function on F sub (n x n).

Download or read book Lacunary Polynomials Over Finite Fields written by László Rédei and published by . This book was released on 1973 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Scalar Polynomial Functions on the Nxn Matrices Over a Finite Field written by Gary L. Wright and published by . This book was released on 1975 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Arithmetic of Finite Fields written by Jean Claude Bajard and published by Springer Nature. This book was released on 2021-02-16 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-workshop proceedings of the 8th International Workshop on the Arithmetic of Finite Field, WAIFI 2020, held in Rennes, France in July 2020. Due to the COVID-19, the workshop was held online. The 12 revised full papers and 3 invited talks presented were carefully reviewed and selected from 22 submissions. The papers are organized in topical sections on invited talks, Finite Field Arithmetic, Coding Theory, Network Security and much more.

Download or read book Linear Methods for Polynomial Factorization Over Finite Fields written by Peter L. A. Roelse and published by . This book was released on 1997 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Topics in Galois Fields written by Dirk Hachenberger and published by Springer Nature. This book was released on 2020-09-29 with total page 785 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a self-contained presentation of the foundations of finite fields, including a detailed treatment of their algebraic closures. It also covers important advanced topics which are not yet found in textbooks: the primitive normal basis theorem, the existence of primitive elements in affine hyperplanes, and the Niederreiter method for factoring polynomials over finite fields. We give streamlined and/or clearer proofs for many fundamental results and treat some classical material in an innovative manner. In particular, we emphasize the interplay between arithmetical and structural results, and we introduce Berlekamp algebras in a novel way which provides a deeper understanding of Berlekamp's celebrated factorization algorithm. The book provides a thorough grounding in finite field theory for graduate students and researchers in mathematics. In view of its emphasis on applicable and computational aspects, it is also useful for readers working in information and communication engineering, for instance, in signal processing, coding theory, cryptography or computer science.

Download or read book Computer Algebra and Polynomials written by Jaime Gutierrez and published by Springer. This book was released on 2015-01-20 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebra and number theory have always been counted among the most beautiful mathematical areas with deep proofs and elegant results. However, for a long time they were not considered that important in view of the lack of real-life applications. This has dramatically changed: nowadays we find applications of algebra and number theory frequently in our daily life. This book focuses on the theory and algorithms for polynomials over various coefficient domains such as a finite field or ring. The operations on polynomials in the focus are factorization, composition and decomposition, basis computation for modules, etc. Algorithms for such operations on polynomials have always been a central interest in computer algebra, as it combines formal (the variables) and algebraic or numeric (the coefficients) aspects. The papers presented were selected from the Workshop on Computer Algebra and Polynomials, which was held in Linz at the Johann Radon Institute for Computational and Applied Mathematics (RICAM) during November 25-29, 2013, at the occasion of the Special Semester on Applications of Algebra and Number Theory.

Download or read book Solving Polynomials Over Finite Fields written by Christopher Wayne Walker and published by . This book was released on 1992 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Handbook of Finite Fields written by Gary L. Mullen and published by CRC Press. This book was released on 2013-06-17 with total page 1048 pages. Available in PDF, EPUB and Kindle. Book excerpt: Poised to become the leading reference in the field, the Handbook of Finite Fields is exclusively devoted to the theory and applications of finite fields. More than 80 international contributors compile state-of-the-art research in this definitive handbook. Edited by two renowned researchers, the book uses a uniform style and format throughout and

Download or read book Permutation Polynomials Over Finite Fields written by Martha Martinez and published by . This book was released on 1997 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Note on Systems of Polynomial Equations Over Finite Fields written by Vincenzo Acciaro and published by . This book was released on 1993 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "Let F be a finite field of q elements and characteristic p (so q = p[superscript n] for some n [> or =] 1) and let [gamma] := [formula] be a system of polynomial equations with coefficients in F. In this paper we relate the structure of the F-algebra [formula] to the roots of [gamma] in F[superscript r]."