Completely Regular Codes In Distance Regular Graphs
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Completely Regular Codes In Distance Regular Graphs
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Author : Minjia Shi
language : en
Publisher: CRC Press
Release Date : 2025-03-14
Completely Regular Codes In Distance Regular Graphs written by Minjia Shi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-14 with Mathematics categories.
The concept of completely regular codes was introduced by Delsarte in his celebrated 1973 thesis, which created the field of Algebraic Combinatorics. This notion was extended by several authors from classical codes over finite fields to codes in distance-regular graphs. Half a century later, there was no book dedicated uniquely to this notion. Most of Delsarte examples were in the Hamming and Johnson graphs. In recent years, many examples were constructed in other distance regular graphs including q-analogues of the previous, and the Doob graph. Completely Regular Codes in Distance Regular Graphs provides, for the first time, a definitive source for the main theoretical notions underpinning this fascinating area of study. It also supplies several useful surveys of constructions using coding theory, design theory and finite geometry in the various families of distance regular graphs of large diameters. Features Written by pioneering experts in the domain Suitable as a research reference at the master’s level Includes extensive tables of completely regular codes in the Hamming graph Features a collection of up-to-date surveys.
Distance Regular Graphs
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Author : Andries E. Brouwer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Distance Regular Graphs written by Andries E. Brouwer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Ever since the discovery of the five platonic solids in ancient times, the study of symmetry and regularity has been one of the most fascinating aspects of mathematics. Quite often the arithmetical regularity properties of an object imply its uniqueness and the existence of many symmetries. This interplay between regularity and symmetry properties of graphs is the theme of this book. Starting from very elementary regularity properties, the concept of a distance-regular graph arises naturally as a common setting for regular graphs which are extremal in one sense or another. Several other important regular combinatorial structures are then shown to be equivalent to special families of distance-regular graphs. Other subjects of more general interest, such as regularity and extremal properties in graphs, association schemes, representations of graphs in euclidean space, groups and geometries of Lie type, groups acting on graphs, and codes are covered independently. Many new results and proofs and more than 750 references increase the encyclopaedic value of this book.
Algebraic Combinatorics
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Author : Chris Godsil
language : en
Publisher: Routledge
Release Date : 2017-10-19
Algebraic Combinatorics written by Chris Godsil and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-19 with Mathematics categories.
This graduate level text is distinguished both by the range of topics and the novelty of the material it treats--more than half of the material in it has previously only appeared in research papers. The first half of this book introduces the characteristic and matchings polynomials of a graph. It is instructive to consider these polynomials together because they have a number of properties in common. The matchings polynomial has links with a number of problems in combinatorial enumeration, particularly some of the current work on the combinatorics of orthogonal polynomials. This connection is discussed at some length, and is also in part the stimulus for the inclusion of chapters on orthogonal polynomials and formal power series. Many of the properties of orthogonal polynomials are derived from properties of characteristic polynomials. The second half of the book introduces the theory of polynomial spaces, which provide easy access to a number of important results in design theory, coding theory and the theory of association schemes. This book should be of interest to second year graduate text/reference in mathematics.
Combinatorics And Graphs
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Author : Richard A. Brualdi
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Combinatorics And Graphs written by Richard A. Brualdi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
A collection of papers presented at the international conference IPM 20--Combinatorics 2009, which includes topics covering permutations, designs, graph minors, graph coloring, graph eigenvalues, distance regular graphs and association schemes, hypergraphs, and arrangements.
Lucas Associative Array Processor
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Author : Christer Fernstrom
language : en
Publisher: Springer Science & Business Media
Release Date : 1986-03
Lucas Associative Array Processor written by Christer Fernstrom and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-03 with Computers categories.
After historical introduction, the aspiration technique and imaging modalities are described. Thereafter, the use of aspiration cytology in the diagnosis and mainly in the sta- ging of urologic cancers is on still not well known appli- cations of the procedure in the staging of some organs (bladder, adrenals, penis, testis and secondary ureteral strictures) are reported.
3rd International Castle Meeting On Coding Theory And Applications
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Author : Joaquim Borges
language : en
Publisher: Univ. Autònoma de Barcelona
Release Date : 2011-09-05
3rd International Castle Meeting On Coding Theory And Applications written by Joaquim Borges and has been published by Univ. Autònoma de Barcelona this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-05 with Education categories.
In 1999, a conference called International Meeting on Coding Theory and Cryptography took place at Mota Castle in Castilia (Spain). The conference had great acceptance within the community of coding theory and cryptography researchers. At that moment, and also nowadays, there are not many international workshops about these topics, at least if we compare with other mathematical and engineering subjects of research. Therefore, the general desire was to continue with more Castle Meetings. However, the following conference did not take place until 2008. In that case, the conference was called II International Castle Meeting on Coding Theory and Applications allowing more topics related to coding theory apart from cryptography. Such conference took place at Mota Castle again and the number of participants was similar to the previous edition. The present edition of the conference, called III International Castle Meeting on Coding Theory and Applications has been held at Cardona Castle in Catalonia (Spain). The number of communications has increased and a number of selected papers will be published in a special issue of the journal Designs, Codes and Cryptography. As in the previous editions, the conference has been of high level with notorious invited speakers and scientic committee members.
Applied Algebra Algebraic Algorithms And Error Correcting Codes
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Author : Llorenc Huguet
language : en
Publisher: Springer Science & Business Media
Release Date : 1989-06-14
Applied Algebra Algebraic Algorithms And Error Correcting Codes written by Llorenc Huguet and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-06-14 with Computers categories.
The present volume contains the proceedings of the AAECC-5 Conference held at Menorca (Balearic Islands), June 15-19, 1987. The annual International AAECC Conference covers a range of topics related to Applied Algebra, Error-Correcting Codes, Finite Algebraic Structures, Computational Methods and Complexity in Algebra and Geometry. For the AAECC-5 Conference 73 papers were presented. Out of these thirty papers were selected for publication in the proceedings. They deal with topics such as error correcting codes (concerning problems of covering radius, decoding methods, expert systems and general results in coding theory), computational algebra, Gröbner basis, complexity, finite algebra and graphs. The proceedings of the 6th conference are published as Vol. 357 of the Lecture Notes in Computer Science.
A Collection Of Contributions In Honour Of Jack Van Lint
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Author : P.J. Cameron
language : en
Publisher: Elsevier
Release Date : 2016-06-06
A Collection Of Contributions In Honour Of Jack Van Lint written by P.J. Cameron and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-06 with Mathematics categories.
This collection of contributions is offered to Jack van Lint on the occasion of his sixtieth birthday and appears simultaneously in the series Topics in Discrete Mathematics and as a special double volume of Discrete Mathematics (Volumes 106/107). It is hoped that the papers selected, all written by experts in their own fields, represent the many interesting areas that together constitute the discipline of Discrete Mathematics. It is in this sphere that van Lint has become the acknowledged master and this expansive volume serves to demonstrate the enormous significance he has had on the development of Discrete Mathematics during the last 30 years.
Coding Theory And Applications
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Author : Angela Barbero
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-05
Coding Theory And Applications written by Angela Barbero and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-05 with Computers categories.
This book constitutes the refereed proceedings of the 2nd International Castle Meeting, ISMCTA 2008, Castillo de la Mota, Medina del Campo, Spain, September 2008. The 14 full papers and 5 invited papers presented were carefully reviewed and selected from 34 submissions for inclusion in the book. The papers cover network coding, quantum codes, group codes, codes and combinatorial structures, agebraic-geometry codes, as well as codes and applications.
Applied Algebra Algebraic Algorithms And Error Correcting Codes
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Author : Shojiro Sakata
language : en
Publisher: Springer Science & Business Media
Release Date : 1991-07-10
Applied Algebra Algebraic Algorithms And Error Correcting Codes written by Shojiro Sakata and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-07-10 with Computers categories.
The AAECC conferences focus on the algebraic aspects of modern computer science, which include the most up-to-date and advanced topics. The topic of error-correcting codes is one where theory and implementation are unified into a subject both of mathematical beauty and of practical importance. Algebraic algorithms are not only interesting theoretically but also important in computer and communication engineering and many other fields. This volume contains the proceedings of the 8th AAECC conference, held in Tokyo in August 1990. Researchers from Europe, America, Japan and other regions of the world presented papers at the conference. The papers present new results of recent theoretical and application-oriented research on applied algebra, algebraic algorithms and error-correcting codes.