عنوان

Covering codes /

شابک

0444825118

شابک

9780444825117

شماره

dltt

عنوان اصلي

Covering codes /

نام عام مواد

[Book]

نام نخستين پديدآور

Gérard Cohen [and others]

محل نشرو پخش و غیره

New York :

نام ناشر، پخش کننده و غيره

Elsevier,

تاریخ نشرو بخش و غیره

1997

نام خاص و کميت اثر

xxi, 542 pages :

ساير جزييات

illustrations ;

ابعاد

23 cm

عنوان فروست

North-Holland mathematical library ;

مشخصه جلد

v. 54

متن يادداشت

Includes bibliographical references (pages 495-536) and index

متن يادداشت

Cover -- Contents -- Preface -- List of Symbols -- List of Tables -- Chapter 1. Introduction -- 1.1 Covering problems -- 1.2 Applications -- Chapter 2. Basic facts -- 2.1 Codes -- 2.2 The MacWilliams identities -- 2.3 Krawtchouk polynomials -- 2.4 Hamming spheres -- 2.5 Finite fields -- 2.6 Families of error-correcting codes -- 2.7 Designs, constant weight codes, graphs -- 2.8 Notes -- Chapter 3. Constructions -- 3.1 Puncturing and adding a parity check bit -- 3.2 Direct sum -- 3.3 Piecewise constant codes -- 3.4 Variations on the (u, u + v) construction -- 3.5 Matrix construction -- 3.6 Cascading -- 3.7 Optimal short nonbinary codes -- 3.8 Simulated annealing and local search -- 3.9 Notes -- Chapter 4. Normality -- 4.1 Amalgamated direct sum -- 4.2 Normality of binary linear codes -- 4.3 Abnormal binary nonlinear codes -- 4.4 Normality of binary nonlinear codes -- 4.5 Blockwise direct sum -- 4.6 Notes -- Chapter 5. Linear constructions -- 5.1 Basic facts about linear covering codes -- 5.2 The case R = 1; examples of small codes -- 5.3 Saving more than one coordinate -- 5.4 Davydov's basic construction -- 5.5 Notes -- Chapter 6. Lower bounds -- 6.1 Bounds for the cardinality of the union of K spheres -- 6.2 Balanced codes -- 6.3 Excess bounds for codes with covering radius one -- 6.4 Excess bounds for codes with arbitrary covering radius -- 6.5 The method of linear inequalities -- 6.6 Table on K (n, R) -- 6.7 Lower bounds for nonbinary codes -- 6.8 Notes -- Chapter 7. Lower bounds for linear codes -- 7.1 Excess bounds for linear codes -- 7.2 Linear codes with covering radius two and three -- 7.3 Tables for linear codes -- 7.4 Notes -- Chapter 8. Upper bounds -- 8.1 Codes with given size and distance -- 8.2 Covering radii of subcodes -- 8.3 Covering radius and dual distance -- 8.4 Notes -- Chapter 9. Reed-Muller codes -- 9.1 Definitions and properties -- 9.2 First order Reed-Muller codes -- 9.3 Reed-Muller codes of order 2 and m -- 3 -- 9.4 Covering radius of Reed-Muller codes of arbitrary order -- 9.5 Notes -- Chapter 10. Algebraic codes -- 10.1 BCH codes: definitions and properties -- 10.2 2-and 3-error-correcting BCH codes -- 10.3 Long BCH codes -- 10.4 Normality of BCH codes -- 10.5 Other algebraic codes -- 10.6 Notes -- Chapter 11. Perfect codes -- 11.1 Perfect linear codes over IFq -- 11.2 A nonexistence result -- 11.3 Enumeration of perfect binary codes -- 11.4 Enumeration of perfect codes over Fq -- 11.5 Mixed codes -- 11.6 Generalizations of perfect codes -- 11.7 Notes -- Chapter 12. Asymptotic bounds -- 12.1 Covering radius of unrestricted codes -- 12.2 Greedy algorithm and good coverings -- 12.3 Covering radius of hnear codes -- 12.4 Density of coverings -- 12.5 Coverings of small size -- 12.6 Bounds on the minimum distance -- T$

بدون عنوان

0

متن يادداشت

The problems of constructing covering codes and of estimating their parameters are the main concern of this book. It provides a unified account of the most recent theory of covering codes and shows how a number of mathematical and engineering issues are related to covering problems. Scientists involved in discrete mathematics, combinatorics, computer science, information theory, geometry, algebra or number theory will find the book of particular significance. It is designed both as an introductory textbook for the beginner and as a reference book for the expert mathematician and engineer. A number of unsolved problems suitable for research projects are also discussed

موضوع مستند نشده

Combinatorial packing and covering

موضوع مستند نشده

code

موضوع مستند نشده

enveloppe convexe

موضوع مستند نشده

espace euclidien

موضوع مستند نشده

géométrie algorithmique

موضوع مستند نشده

recouvrement

شماره

ويراست

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

Cohen, G., (Gérard),1951-

تاريخ عمليات

20160203143933.0

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y