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Covering Codes

Volume 54

By: G. Cohen, I. Honkala, S. Litsyn

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Hardcover | 8 November 2005

At a Glance

Hardcover
568 Pages

Dimensions(cm)
23.39 x 15.6 x 3.18

Hardcover

$504.75

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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.

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You Can Find This Book In

Non-Fiction Mathematics Combinatorics & Graph Theory Science Physics Engineering & Technology Technology in General Maths for Engineers Algebra Science in General Maths for Scientists Computing & I.T.

Computer Science Discrete Mathematics Number Theory Applied Mathematics

Introduction
Covering problems
Applications
Basic Facts
Codes
The MacWilliams identities
Krawtchouk polynomials
Hamming spheres
Finite fields
Families of error-correcting codes
Designs, constant weight codes, graphs
Constructions
Puncturing and adding a parity check bit
Direct sum
Piecewise constant codes
Variations on the (u, u + v) construction
Matrix construction
Cascading
Optimal short nonbinary codes
Simulated annealing and local search
Normality
Amalgamated direct sum
Normality of binary linear codes
Abnormal binary nonlinear codes
Normality of binary nonlinear codes
Blockwise direct sum
Linear Constructions
Basic facts about linear covering codes
The case R=1; examples of small codes
Saving more than one coordinate
Davydov's basic construction
Lower Bounds
Bounds for the cardinality of the union of K spheres
Balanced codes
Excess bounds for codes with covering radius one
Excess bounds for codes with arbitrary covering radius
The method of linear inequalities
Table on K(n,R)
Lower bounds for nonbinary codes
Lower Bounds for Linear Codes
Excess bounds for linear codes
Linear codes with covering radius two and three
Tables for linear codes
Upper Bounds
Codes with given size and distance
Covering radii of subcodes
Covering radius and dual distance
Reed-Muller Codes
Definitions and properties
First order Reed-Muller codes
Reed-Muller codes of order 2 and m-3
Covering radius of Reed-Muller codes of arbitrary order
Algebraic Codes
BCH codes: definitions and properties
2- and 3-error-correcting BCH codes
Long BCH codes
Normality of BCH codes
Other algebraic codes
Perfect Codes
Perfect linear codes over IF q
A nonexistence result
Enumeration of perfect binary codes
Enumeration of perfect codes over IF q
Mixed codes
Generalizations of perfect codes
Asymptotic Bounds
Covering radius of unrestricted codes
Greedy algorithm and good coverings
Covering radius of linear codes
Density of coverings
Coverings of small size
Bounds on the minimum distance
Covering radius as a function of dual distance
Packing radius vs covering radius
Weighted Coverings
Basic notions
Lloyd theorem for perfect weighted coverings
Perfect weighted coverings with radius one
Weighted coverings and nonexistence results
Multiple Coverings
Definitions
Perfect multiple coverings
Normality of multiple coverings
Constructions
Tables for multiple coverings
Multiple coverings of deep holes
Football Pools
Constructions for mixed binary/ternary codes
Tables for mixed binary/ternary codes
on the early history of the ternary Golay code
Tilings
Preliminaries
A sufficient condition
Small tiles
Periodicity of tilings
Recursive decomposition of tilings
Tilings and perfect binary codes
Nonexistence results
Writing on Constrained Memories
Worst case coverings and WOMs
The error case
A model for correcting single errors
Single-error-correcting WOM-codes
Nonlinear WOM-codes
Subset Sums and Constrained Memories
Cayley graphs
Subset sums
Maximal sum-free sets
Constrained memories (W*Ms)
Translation-invariant constraints
Domatic number and reluctant memories
Defective memories
The error case
Heterodox Coverings
Perfect coverings by L-spheres
Perfect coverings by spheres of two radii
Coverings by spheres all of different radii
Multicovering radius
Perfect coverings of a sphere and constant weight coverings
Complexity
Table of Contents provided by Publisher. All Rights Reserved.

Covering Codes

Volume 54

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

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