Journal ArticleDOI
Football Pools A Game for Mathematicians
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In this article, the authors proposed a combinatorial approach to the problem of generating arrays of numbers with special features, which is a natural and mathematically easy problem to formulate, but is highly nontrivial and can be attacked using powerful combinators.Abstract:
have some nice, relevant properties. At the same time another group of people combinatorialists are busy trying to produce many different types of arrays of numbers with special features. We have the feeling that the two groups are not well acquwainted with each other's work, although recently some mathematical journals have published papers reporting results obtained by the playing community, and we hope that this paper will contribute to increasing the mathematicians' interest in these problems. The problems are natural and mathematically easy to formulate, but are highly nontrivial and can be attacked using powerful combinatorial machinery.read more
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Book ChapterDOI
Symmetry in Integer Linear Programming
TL;DR: This paper reviews techniques developed to take advantage of the symmetry in an ILP during its solution, and surveys related topics, such as symmetry detection, polyhedral studies of symmetric ILPs, and enumeration of all non isomorphic optimal solutions.
Journal ArticleDOI
Orbital branching
TL;DR: The resulting method, orbital branching, is shown to be quite competitive with a similar method known as isomorphism pruning and significantly better than a state-of-the-art commercial solver on symmetric integer programs.
Journal ArticleDOI
Bounds on mixed binary/ternary codes
TL;DR: The upper bounds are obtained by applying the linear programming bound to the product of two association schemes and the lower bounds arise from a number of different constructions.
Book ChapterDOI
Orbital Branching
TL;DR: The resulting method is shown to be quite competitive with a similar method known as isomorphism pruningand significantly better than a state-of-the-art commercial solver on symmetric integer programs.
Journal ArticleDOI
Comments on "An inequality on guessing and its application to sequential decoding"
TL;DR: It is shown that one can tighten this bound for the case of positive integer moments (when /spl rho/=1, the bound is improved by a factor of 2) and that the new bound also applies to a class of nonminimal guessing sequences.
References
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Book
The Theory of Error-Correcting Codes
TL;DR: This book presents an introduction to BCH Codes and Finite Fields, and methods for Combining Codes, and discusses self-dual Codes and Invariant Theory, as well as nonlinear Codes, Hadamard Matrices, Designs and the Golay Code.
Book
Sphere packings, lattices, and groups
TL;DR: The second edition of this book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space?
Introduction to coding theory
TL;DR: This third edition has been revised and expanded, including new chapters on algebraic geometry, new classes of codes, and the essentials of the most recent developments on binary codes.
Book
Introduction to the Theory of Error-Correcting Codes
TL;DR: In this paper, a double-error-correcting BCH Code and a Finite Field of 16 Elements (FF16E) were proposed to correct the double error of the BCH code.