Covering Codes (North-Holland Mathematical Library)

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    • Chapter 12 is devoted to asymptotical covering radius problems.

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    The next two chapters discuss natural generalizations of the covering radius problem, like weighted coverings, multiple coverings and multiple coverings of deep holes. Chapter 15 deals with a more recreational application, namely, how to use covering codes in connection with football pools. Chapter 16 studies partitions of the binary space into tiles, i. In the next chapter, we study a general model of constrained memories; it turns out to rely on the worst-case behaviour of the covering radius of shortened codes.

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    In Chapter 18 we explore the connections between graphs, groups and codes and how spe- cific techniques pertaining to these three areas are intertwined. Chapter 19 is devoted to variations on the theme of perfect coverings by spheres, namely coverings by unions of shells, by spheres of two or more radii, or by spheres all of different radii.

    In Chapter 20 we study various complexity issues related to the field. A natural packing problem in the conventional n-dimensional euchdean space is to ask for the maximal number of identical non-intersecting spheres in a large volume. This has a number of interesting connections to differ- ent areas of mathematics like geometry, group theory, number theory and quadratic forms. At the same time it has important engineering apphcations like constructing signals for communication systems. The covering problem in the euclidean space asks for the minimal number of identical spheres needed to cover a large volume.

    For example, in a mobile radio network, minimizing the required number of base stations whose range is given, typically 10 km, is a covering problem in the two-dimensional euclidean space. The covering and packing problems in the euclidean space have been ex- tensively studied, see, e. The same issues can be considered in the n-dimensional Hamming space consisting of binary words, i. The elements of the Hamming space are also called points.

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    In con- trast to the euclidean space, the number of points in this space is finite. An arbitrary nonempty subset of the Hamming space is called a code, and its elements are called codewords. The Hamming distance between two vectors is the number of coordinates components in which the vectors differ.

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    The minimum distance of a code is the smallest of the pairwise distances between the codewords. In a natural way the sphere of radius r consists of all the vectors within distance r from the centre.

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    For example, the sphere of radius one with centre ill the five-dimensional Hamming space consists of the vectors , , , , , Introduction Now we can formulate the following two questions. Given n and r, what is the maximal number of non-intersecting Hamming spheres of radius r that can be placed in the n-dimensional Hamming space? Learn more about Amazon Prime. Get fast, free shipping with Amazon Prime.

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    Buy Covering Codes, Volume 54 (North-Holland Mathematical Library) on www.farmersmarketmusic.com ✓ FREE SHIPPING on qualified orders. Covering Codes (North-Holland Mathematical Library Book 54) eBook: G. Cohen , I. Honkala, S. Litsyn, A. Lobstein: www.farmersmarketmusic.com: Kindle Store.

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    AmazonGlobal Ship Orders Internationally. Amazon Inspire Digital Educational Resources. Amazon Rapids Fun stories for kids on the go. The problems of constructing covering codes and of estimating their parameters are the main concern of this book. 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. Chapter 2 Basic facts.

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    Chapter 2 Basic facts. Information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be made in the U. Such a set is called a covering code or simply a covering in what follows. The chapters are fairly independent, which should allow nonlinear reading. Don't have a Kindle? The problems of constructing covering codes and of estimating their parameters are the main concern of this book. Linear Algebra and Linear Models.

    Chapter 5 Linear constructions. Chapter 6 Lower bounds. Chapter 7 Lower bounds for linear codes.