2 edition of **algebraic approach to the association schemes of coding theory.** found in the catalog.

algebraic approach to the association schemes of coding theory.

P. Delsarte

- 57 Want to read
- 18 Currently reading

Published
**1973**
by N.V. Philips" Gloeilampenfabrieken in Eindhoven
.

Written in English

**Edition Notes**

Series | Philips research reports supplements, 1973 -- no. 10 |

ID Numbers | |
---|---|

Open Library | OL19660297M |

An algebraic approach to the association schemes of coding theory,” (). An extension of the triangular association scheme to three associate classes,”. An algebraic approach to the association schemes of coding theory by P. Delsarte; 1 edition; First published in

Algebraic Coding Theory Elwyn R Berlekamp This is the revised edition of Berlekamp's famous book, "Algebraic Coding Theory", originally published in , wherein he introduced several algorithms which have subsequently dominated engineering practice in this field. An algebraic approach to association schemes and coding theory. Article. The present work is a contribution to the algebraic theory of association schemes, where special emphasis is put on.

The theme of association schemes is represented by new classification results and new classes of schemes related to posets. This volume collects up-to-date applications of the theory of association schemes to coding and presents new properties of both polynomial and general association schemes. Algebraic Coding Theory Over Finite Commutative Rings | Steven T. Dougherty (auth.) | download | B–OK. Download books for free. Find books.

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An Introduction to Association Schemes and Coding Theory N. Sloane ABSTRACT Association schemes originated in s t a t i s t i c s, but have recently been used in coding theory and combinatorics by Delsarte, McEliece and others to obtain strong upper bounds on the size of codes and other combinatorial objects, and to characterize those objects (such a s perfect codes) Cited by: Get this from a library.

An algebraic approach to the association schemes of coding theory. [P Delsarte]. An Algebraic Approach to the Association Schemes of Coding Theory Philips journal of research / Supplement, Philips' Gloeilampenfabrieken (Eindhoven.) Issue 10 of Philips research reports: Supplements, Supplements, ISSN Supplements: Philips research reports, Philips' Gloeilampenfabrieken Eindhoven: Author: P.

Delsarte: Publisher5/5(1). Association algebraic approach to the association schemes of coding theory. book provide the appropriate setting for treating certain problems from several different areas of algebraic combinatorics, for example, coding theory, design theory, algebraic graph theory, finite group theory, and finite geometry.

The following definition is equivalent to that of Delsarte (). Cite this paper as: Delsarte P. () The Association Schemes of Coding Theory. In: Hall M., van Lint J.H. (eds) Combinatorics. NATO Advanced Study Institutes Series (Series C — Mathematical and Physical Sciences), vol Cited by: The primary object of the lecture notes is to develop a treatment of association schemes analogous to that which has been so successful in the theory of finite groups.

The main chapters are decomposition theory, representation theory, and the theory of generators. Tits buildings come into play when.

The Hamming scheme and the Johnson scheme, are two examples that are of major significance in classical coding theory.

Association scheme theory is part of what is now called algebraic combinatorics. An important example, which belongs to association scheme theory, is the distinction between distance-regular graphs and distance-transitive graphs.

Coding theory is the study of the properties of codes and their fitness for a specific application. Codes are used for data compression, cryptography, error-correction, and networking. Codes are studied by various scientific disciplines—such as information theory, electrical engineering, mathematics, linguistics, and computer science—for the purpose of designing efficient and reliable data.

The book is unique in presenting algorithms, architectures, and applications of coding theory in a unified framework. It covers the basics of coding theory before moving on to discuss algebraic linear block and cyclic codes, turbo codes and low.

Abstract. Association schemes were originally introduced by Bose and his co-workers in the design of statistical experiments. Since that point of incep-tion, the concept has proved useful in the study of group actions, in algebraic graph theory, in algebraic coding theory, and in areas as far aﬁeld as knot theory and numerical integration.

R.C. BOSE and D.M. MESNER () "On linear associative algebras corresponding to association schemes of partially balanced designs" Ann. Math. Statist. 10 p. 21– Google Scholar [8]. Thus in coding theory we look for codes that are as large as possible, since such codes are most effective in transmitting information over noisy channels.

The theory of association schemes provides the most effective means for determining just how large is actually possible; this theory rests on Delsarte’s thesis [4], which showed how to use. We study self-dual codes over certain finite rings which are quotients of quadratic imaginary fields or of totally definite quaternion fields over Q.A natural weight taking two different nonzero values is defined over these rings; using invariant theory, we give a basis for the space of invariants to which belongs the three variables weight enumerator of a self-dual code.

Covering topics in algebraic geometry, coding theory, and cryptography, this volume presents interdisciplinary group research completed for the February conference at the Institute for Pure and Applied Mathematics (IPAM) in cooperation with the Association for Women in Mathematics (AWM).

An algebraic approach to the association schemes of coding theory, Philips Res. Rep. Suppl. 10 (). studies codes and designs within the unifying framework of association schemes; has been playing a central role in Algebraic Combinatorics; is still important.

Applications include extremal set theory and ﬁnite geometry. The theory of association schemes arose in statistics, in the theory of experimental design for the analysis of variance. In mathematics, association schemes belong to both algebra andin algebraic combinatorics, association schemes provide a unified approach to many topics, for example combinatorial designs and coding theory.

In algebra, association schemes. An algebraic approach to the association schemes of coding theory. by P Delsarte. Format: Thesis, Dissertation Publication year: Held by WUR Library. Coding theory. Numerical analysis. Codierung; Kombinatorik; Academic theses. statistische analyse; statistical analysis; Statistical Analysis.

Using a simple yet rigorous approach, Algebraic and Stochastic Coding Theory makes the subject of coding theory easy to understand for readers with a thorough knowledge of digital arithmetic, Boolean and modern algebra, and probability theory.

It explains the underlying principles of coding theory and offers a clear, detailed description of. This paper contains a survey of association scheme theory (with its algebraic and analytical aspects) and of its applications to coding theory (in a wide sense).

It is mainly concerned with a class of subjects that involve the central notion of the distance distribution of a code. This chapter introduces and elaborates on the fruitful interplay of coding theory and algebraic combinatorics, with most of the focus on the interaction of codes with combinatorial designs, finite.

Among the topics discussed are universal data compression, graph theoretical ideas in the construction of codes and lattices, decoding algorithms, and computation of capacity in various communications schemes.

The book is suitable for graduate students and researchers interested in coding and information theory.Cliques in association schemes 29 The Elias theorem 29 The linear-programming bound 31 Designs in association schemes 32 Characteristic matrices 35 4. AN INTRODUCTION TO ALGEBRAIC CODING THEORY.

37 The Hamming schemes 37 Eigenmatrices and Krawtchouk polynomials 37 Codes in Hamming schemes 40 P. Delsarte: An Algebraic Approach to the Association Schemes of Coding Theory (Phillips Research Reports ).

[on Bill Martin's web site (with permission).] J. Matousek: Using the Borsuk-Ulam Theorem (Springer ).