The explanation of the formal duality of Kerdock and Preparata codes - one of the outstanding recent results in applied algebra - is related to the discovery of large sets of quadriphase sequences over Z4 whose correlation properties are better than those of the best binary sequences. Moreover, the correlation properties of sequences are closely related to difference properties of certain sets in (cyclic) groups. Most of the articles collected here contain descriptions of the connection between difference sets, sequences and correlation properties of sequences. There are two more elementary introductory articles: an introduction to difference sets (by two of the editors), and an introduction to the correlation of sequences (by Solomon Golomb).
Difference Sets, Sequences and Their Correlation Properties
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Key Phrases - Statistically Improbable Phrases (SIPs):
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sonar sequences, nonzero character sum, inequivalent difference sets, relative difference sets, cyclic difference sets, abelian difference sets, circulant weighing matrices, divisible difference sets, monomial hyperovals, planar difference sets, favorable correlation properties, new difference sets, largest direct factors, spanning ruler, ternary arrays, asymptotic merit factor, group ring element, combiner function, nonlinear binary codes, perfect binary arrays, symplectic spread, permutation polynomials, correlation immunity, aperiodic correlations, keystream bits Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Computer Science, Kluwer Academic Publishers, Cambridge University Press, Discrete Math, Finite Fields Appl, London Math, University of Richmond, Ars Combinatoria, Combinatorial Theory, Handbook of Coding Theory, San Francisco, Soviet Math, Technical Report, The Theory of Error-Correcting Codes, Utilitas Math New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
sonar sequences, nonzero character sum, inequivalent difference sets, relative difference sets, cyclic difference sets, abelian difference sets, circulant weighing matrices, divisible difference sets, monomial hyperovals, planar difference sets, favorable correlation properties, new difference sets, largest direct factors, spanning ruler, ternary arrays, asymptotic merit factor, group ring element, combiner function, nonlinear binary codes, perfect binary arrays, symplectic spread, permutation polynomials, correlation immunity, aperiodic correlations, keystream bits Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Computer Science, Kluwer Academic Publishers, Cambridge University Press, Discrete Math, Finite Fields Appl, London Math, University of Richmond, Ars Combinatoria, Combinatorial Theory, Handbook of Coding Theory, San Francisco, Soviet Math, Technical Report, The Theory of Error-Correcting Codes, Utilitas Math New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 35
books:
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4
books
cite this book:
- Finite Geometry and Character Theory (Lecture Notes in Mathematics) by Alexander Pott on 5 pages
- The Theory of Error-Correcting Codes (North-Holland Mathematical Library) by F.J. MacWilliams on 4 pages
- Design Theory: Volume 1 (Encyclopedia of Mathematics and its Applications) by Thomas Beth on page 111, page 352, and Back Matter
- Symmetric Designs: An Algebraic Approach (London Mathematical Society Lecture Note Series) by Eric S. Lander on page 239, page 257, and page 294
- Finite Fields (Encyclopedia of Mathematics and its Applications) by Rudolf Lidl on page 225, page 391, and Back Matter
See all 35 books this book cites
- Hadamard Matrices and Their Applications by K. J. Horadam on 4 pages
- Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar by Solomon W. Golomb in Front Matter, Back Matter (1), and Back Matter (2)
- Sequences and Their Applications - SETA 2004: Third International Conference, Seoul, Korea, October 24-28, 2004, Revised Selected Papers (Lecture ... Computer Science and General Issues) by Tor Helleseth on page 54, and page 55
- Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 16th International Symposium, AAECC-16, Las Vegas, NV, USA, February 20-24, 2006, ... Computer Science and General Issues) by Marc Fossorier on page 59
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