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The explanation of the formal duality of Kerdock and Preparata codes is one of the outstanding results in the field of applied algebra in the last few years. This result is related to the discovery of large sets of quad riphase 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. It is the purpose of this book to illustrate the connection between these three topics. Most articles grew out of lectures given at the NATO Ad vanced Study Institute on "Difference sets, sequences and their correlation properties". This workshop took place in Bad Windsheim (Germany) in August 1998. The editors thank the NATO Scientific Affairs Division for the generous support of this workshop. Without this support, the present collection of articles would not have been realized.
Table des matières
Perfect Ternary Arrays.- Stream Ciphers and Correlation.- Error Correcting Codes, Correlation and Quantum Engtanglement.- A Unified Approach to Difference Sets with gcd (v, n) > 1.- Codes, Correlations and Power Control in OFDM.- Kasami Power Functions, Permutation Polynomials and Cyclic Difference Sets.- Construction of Signals with Favorable Correlation Properties.- Codes and Sequences over ?4 - A Tutorial Overview.- The Merit Factor of Binary Sequences.- Lander's Tables are Complete!.- Difference Sets: An Introduction.- Applications of Difference Sets to the Aperture Design in Multielement Systems in Radio Science and Astronomy.- Constructive Representation Theoretic Methods and Non-Abelian Difference Sets.- Survey of Results on Signal Patterns for Locating One or Multiple Targets.- Sequence Design for CDMA Systems - Mean-Square Correlation Properties of Sequence Families.- Bent Functions and Coding Theory.- Recent Results on Difference Sets with Classical Parameters.
Résumé
Proceedings of the NATO Advanced Study Institute on Difference Sets, Sequence and their Correlation Properties, Bad Winsheim, 2-14 August 1998
