Ronald C. Mullin's Books

An Introduction to Algebraic and Combinatorial Coding Theory

By: Ian F. Blake,Ronald C. Mullin

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An Introduction to Algebraic and Combinatorial Coding Theory

By: Ian F. Blake,Ronald C. Mullin

An Introduction to Algebraic and Combinatorial Coding Theory focuses on the principles, operations, and approaches involved in the combinatorial coding theory, including linear transformations, chain groups, vector spaces, and combinatorial constructions. The publication first offers information on finite fields and coding theory and combinatorial constructions and coding. Discussions focus on quadratic residues and codes, self-dual and quasicyclic codes, balanced incomplete block designs and codes, polynomial approach to coding, and linear transformations of vector spaces over finite fields. The text then examines coding and combinatorics, including chains and chain groups, equidistant codes, matroids, graphs, and coding, matroids, and dual chain groups. The manuscript also ponders on Möbius inversion formula, Lucas's theorem, and Mathieu groups. The publication is a valuable source of information for mathematicians and researchers interested in the combinatorial coding theory.

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Page Count

244

Publisher

Academic Press

Published Date

ISBN 10

1483260291

ISBN 13

9781483260297

Applications of Finite Fields

By: Alfred J. Menezes,Ian F. Blake,XuHong Gao,Ronald C. Mullin,Scott A. Vanstone,Tomik Yaghoobian

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Applications of Finite Fields

By: Alfred J. Menezes,Ian F. Blake,XuHong Gao,Ronald C. Mullin,Scott A. Vanstone,Tomik Yaghoobian

The theory of finite fields, whose origins can be traced back to the works of Gauss and Galois, has played a part in various branches in mathematics. Inrecent years we have witnessed a resurgence of interest in finite fields, and this is partly due to important applications in coding theory and cryptography. The purpose of this book is to introduce the reader to some of these recent developments. It should be of interest to a wide range of students, researchers and practitioners in the disciplines of computer science, engineering and mathematics. We shall focus our attention on some specific recent developments in the theory and applications of finite fields. While the topics selected are treated in some depth, we have not attempted to be encyclopedic. Among the topics studied are different methods of representing the elements of a finite field (including normal bases and optimal normal bases), algorithms for factoring polynomials over finite fields, methods for constructing irreducible polynomials, the discrete logarithm problem and its implications to cryptography, the use of elliptic curves in constructing public key cryptosystems, and the uses of algebraic geometry in constructing good error-correcting codes. To limit the size of the volume we have been forced to omit some important applications of finite fields. Some of these missing applications are briefly mentioned in the Appendix along with some key references.

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Page Count

229

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1475722265

ISBN 13

9781475722260

The Mathematical Theory of Coding

By: Ian F. Blake,Ronald C. Mullin

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The Mathematical Theory of Coding

By: Ian F. Blake,Ronald C. Mullin

The Mathematical Theory of Coding focuses on the application of algebraic and combinatoric methods to the coding theory, including linear transformations, vector spaces, and combinatorics. The publication first offers information on finite fields and coding theory and combinatorial constructions and coding. Discussions focus on self-dual and quasicyclic codes, quadratic residues and codes, balanced incomplete block designs and codes, bounds on code dictionaries, code invariance under permutation groups, and linear transformations of vector spaces over finite fields. The text then takes a look at coding and combinatorics and the structure of semisimple rings. Topics include structure of cyclic codes and semisimple rings, group algebra and group characters, rings, ideals, and the minimum condition, chains and chain groups, dual chain groups, and matroids, graphs, and coding. The book ponders on group representations and group codes for the Gaussian channel, including distance properties of group codes, initial vector problem, modules, group algebras, andrepresentations, orthogonality relationships and properties of group characters, and representation of groups. The manuscript is a valuable source of data for mathematicians and researchers interested in the mathematical theory of coding.

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Page Count

369

Publisher

Academic Press

Published Date

ISBN 10

1483260593

ISBN 13

9781483260594

Finite Fields: Theory, Applications and Algorithms

Theory, Applications, and Algorithms : Fourth International Conference on Finite Fields-- Theory, Applications, and Algorithms, August 12-15, 1997, University of Waterloo, Ontario, Canada

By: Ronald Cleveland Mullin,Gary L. Mullen

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Finite Fields: Theory, Applications and Algorithms

Theory, Applications, and Algorithms : Fourth International Conference on Finite Fields-- Theory, Applications, and Algorithms, August 12-15, 1997, University of Waterloo, Ontario, Canada

By: Ronald Cleveland Mullin,Gary L. Mullen

The Ontario conference drew workers from theoretical, applied, and algorithm finite field theory to share their recent findings applying finite fields to such areas as number theory, algebra, and algebraic geometry. The 21 topics include actions of linearized polynomials on the algebraic closure of a finite field, kernels and defaults, computing zeta functions over finite fields, and the state complexity of some long codes. No index. Member prices are $39 for institutions and $29 for individuals. Annotation copyrighted by Book News, Inc., Portland, OR

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Page Count

258

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821808176

ISBN 13

9780821808177

Book's by Ronald C. Mullin

An Introduction to Algebraic and Combinatorial Coding Theory

An Introduction to Algebraic and Combinatorial Coding Theory

Applications of Finite Fields

Applications of Finite Fields

The Mathematical Theory of Coding

The Mathematical Theory of Coding

Finite Fields: Theory, Applications and Algorithms

Finite Fields: Theory, Applications and Algorithms

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