Muutke küpsiste eelistusi

E-raamat: Error-Correcting Linear Codes: Classification by Isometry and Applications

4.00/5 (2 hinnangut Goodreads-ist)
, , , , ,
Teised raamatud teemal:
  • Formaat - PDF+DRM
  • Hind: 111,14 €*
  • * hind on lõplik, st. muud allahindlused enam ei rakendu
  • Lisa ostukorvi
  • Lisa soovinimekirja
  • See e-raamat on mõeldud ainult isiklikuks kasutamiseks. E-raamatuid ei saa tagastada.
Error-Correcting Linear Codes: Classification by Isometry and ApplicationsSuurem pilt
Teised raamatud teemal:

DRM piirangud

  • Kopeerimine (copy/paste):

    ei ole lubatud

  • Printimine:

    ei ole lubatud

  • Kasutamine:

    Digitaalõiguste kaitse (DRM)
    Kirjastus on väljastanud selle e-raamatu krüpteeritud kujul, mis tähendab, et selle lugemiseks peate installeerima spetsiaalse tarkvara. Samuti peate looma endale  Adobe ID Rohkem infot siin. E-raamatut saab lugeda 1 kasutaja ning alla laadida kuni 6'de seadmesse (kõik autoriseeritud sama Adobe ID-ga).

    Vajalik tarkvara
    Mobiilsetes seadmetes (telefon või tahvelarvuti) lugemiseks peate installeerima selle tasuta rakenduse: PocketBook Reader (iOS / Android)

    PC või Mac seadmes lugemiseks peate installima Adobe Digital Editionsi (Seeon tasuta rakendus spetsiaalselt e-raamatute lugemiseks. Seda ei tohi segamini ajada Adober Reader'iga, mis tõenäoliselt on juba teie arvutisse installeeritud )

    Seda e-raamatut ei saa lugeda Amazon Kindle's. 

This text offers an introduction to error-correcting linear codes for graduate students in mathematics, computer science and engineering and researchers. The book differs from other standard texts in its emphasis on the classification of codes by means of isometry classes. It rigorously develops the relevant algebraic concepts like finite fields and group actions. In addition, coverage also discusses in cyclic codes in great detail as well as their application in CD players.

This text offers an introduction to error-correcting linear codes for graduate students in mathematics, computer science and engineering and researchers. The book differs from other standard texts in its emphasis on the classification of codes by means of isometry classes. The relevant algebraic concepts like finite fields and group actions are developed rigorously. Cyclic codes are discussed in great detail, as well as their application in CD players. In the last four chapters these isometry classes are enumerated, and representatives are constructed algorithmically with or without a prescribed automorphism group. Furthermore, lattice basis reduction is presented as a tool for computing generator matrices and the minimum distance of codes. The attached CD provides access to generator matrices of more than 70000 nonisometric optimal codes, covering all optimal codes for a given set of code parameters. It also contains software for evaluating minimum distances, weight enumerators, and for the construction of codes.

Arvustused

From the reviews:





"The theory of error-correcting codes is a new addition to the list of mathematical disciplines. This book contains 51 figures and 102 tables. The book provides access to all results at a level which is proper for graduate students of mathematics and computer science as well as for researchers." (Zlatko Varbanov, Zentralblatt MATH, Vol. 1102 (4), 2007)

"This is a thorough treatment of the theory of error-correcting codes. This book is remarkable because of the enormous amount of material presented (in a very lucid style), but also because of the great variety of mathematical disciplines used . A beautiful book on applied mathematics!" (H. Mitsch, Monatshefte für Mathematik, Vol. 151 (3), 2007)

"The main object of the book under review is an error-correcting linear code. a motivated reader can profit much from studying this monograph, which contains rich material in one of the rapidly developing areas. The presentation of material is reader-friendly, arguments are clear and concise, numerous exercises are original and stimulating . To sum up, the book under review can be strongly recommended to anyone interested in the topic." (Boris È. Kunyavskii, Mathematical Reviews, Issue 2008 h)

Preface V
Table of Contents XI
List of Tables XV
List of Figures XIX
List of Symbols XXI
1 Linear Codes
1.1 Introduction
3(8)
1.2 Linear Codes, Encoding and Decoding
11(9)
1.3 Check Matrices and the Dual Code
20(8)
1.4 Classification by Isometry
28(13)
1.5 Semilinear Isometry Classes of Linear Codes
41(10)
1.6 The Weight Enumerator
51(14)
1.7 Systematic Encoding, Information Sets
65(5)
1.8 A Minimum Distance Algorithm
70(12)
2 Bounds and Modifications
2.1 Combinatorial Bounds for the Parameters
82(12)
2.2 New Codes from Old and the Minimum Distance
94(8)
2.3 Further Modifications and Constructions
102(16)
2.4 Reed–Muller-Codes
118(10)
2.5 MDS-Codes
128(11)
3 Finite Fields
3.1 Finite Fields – An Introduction
139(10)
3.2 Existence and Uniqueness of Finite Fields
149(18)
3.3 The Galois Group and Normal Bases
167(3)
3.4 Enumeration under Group Actions, Lyndon Words
170(12)
3.5 Construction of Irreducible Polynomials
182(21)
3.6 Representations of Field Elements
203(2)
3.7 Projective Geometry
205(9)
4 Cyclic Codes
4.1 Cyclic Codes as Group Algebra Codes
214(6)
4.2 Polynomial Representation of Cyclic Codes
220(17)
4.3 BCH-Codes and Reed–Solomon-Codes
237(15)
4.4 Quadratic-Residue-Codes, Golay-Codes
252(16)
4.5 Idempotents and the Discrete Fourier Transform
268(17)
4.6 Alternant-Codes, Goppa-Codes
285(7)
4.7 The Structure Theorem
292(19)
4.8 Codes of p-Power Block Length
311(8)
4.9 Bounds for the Minimum Distance
319(8)
4.10 Reed-Muller-Codes
327(7)
4.11 Encoding
334(4)
4.12 Permutation Decoding
338(8)
4.13 Error-Correcting Pairs
346(4)
4.14 Majority Logic Decoding
350(20)
5 Mathematics and Audio Compact Discs
5.1 Fourier Transform, Shannon's Sampling Theorem
370(19)
5.2 Correction of Erasures
389(12)
5.3 Burst Errors and Interleaving of Codes
401(22)
5.4 More Details on Compact Discs
423(12)
5.5 More Details on CD-ROM
435(9)
6 Enumeration of Isometry Classes
6.1 Enumeration of Linear Isometry Classes
444(19)
6.2 Indecomposable Linear Codes
463(13)
6.3 Cycle Indices of Projective Linear Groups
476(23)
6.4 Numerical Data for Linear Isometry Classes
499(12)
6.5 Critical Codes
511(16)
6.6 Random Generation of Linear Codes
527(5)
6.7 Enumeration of Semilinear Isometry Classes
532(17)
6.8 Local Isometries
549(4)
6.9 Existence and Construction of Normal Bases
553(12)
7 Solving Systems of Diophantine Linear Equations
7.1 Lattices
565(3)
7.2 Diophantine Equations and Lattices
568(6)
7.3 Basic Theory of Lattices
574(3)
7.4 Gram-Schmidt Orthogonalization
577(2)
7.5 Bounds on Lattice Vectors
579(7)
7.6 Lattice Basis Reduction
586(12)
7.7 Lattice Point Enumeration
598(7)
7.8 Computing the Minimum Distance of Linear Codes
605(11)
8 Linear Codes with a Prescribed Minimum Distance
8.1 Minihypers
616(9)
8.2 Group Actions on Lattices
625(12)
8.3 Prescribing a Group of Automorphisms
637(3)
8.4 Linear Codes of Prescribed Type
640(4)
8.5 Numerical Results
644(20)
9 The General Case
9.1 The Problem
664(5)
9.2 Computing with Permutation Groups
669(7)
9.3 A Permutation Representation
676(6)
9.4 The Lexicographical Order
682(6)
9.5 Orderly Generation of Codes
688(12)
9.6 The Algorithm Snakes and Ladders
700(17)
9.7 Base and Strong Generating Sets
717(10)
9.8 The Projective Linear Group
727(11)
9.9 The Projective Semilinear Group
738(3)
9.10 Numerical Data
741(14)
A Appendix: The Attached Compact Disc
A.1 System Requirements
755(1)
A.2 The Installation
755(1)
A.3 The Programs
756(1)
A.4 The Dynamic Tables
757(1)
A.5 The Precomputed Tables: Enumerative Results
758(1)
A.6 The Precomputed Tables: Optimal Linear Codes
759(4)
A.7 The Programs for
Chapter 9
763(8)
References 771(14)
Index 785


Lisainfo e-raamatute kohta Lisainfo e-raamatute kohta
Püsilink: https://www.kriso.ee/db/97835403170362e.html
Märksõnad: