Difference Sets, Sequences and their Correlation Properties / Edition 1by A. Pott
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… See more details below
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).
Table of ContentsPreface. Perfect Ternary Arrays; K.T. Arasu, J.F. Dillon. Stream Ciphers and Correlation; K. Brincat, et al. Error Correcting Codes, Correlation and Quantum Entanglement; A.R. Calderbank. A Unified Approach to Difference Sets with ged (v, n)>1; J.A. Davis, J. Jedwab. Codes, Correlations and Power Control in OFDM; J.A. Davis, et al. Kasami Power Functions, Permutation Polynomials and Cyclic Difference Sets; H. Dobbertin. Construction of Signals with Favorable Correlations Properties; S.W. Golomb. Codes and Sequences over Zeta4 - A Tutorial Overview; T. Helleseth, P.V. Kumar. The Merit Factor of Binary Sequences; T. Høholdt. Lander's Tables are Complete! J.E. Iiams. Difference Sets: An Introduction; D. Jungnickel, A. Pott. Applications of Difference Sets to the Aperture Design in Multielement Systems in Radio Science and Astronomy; L.E. Kopilovich. Constructive Representation Theoretic Methods and Non-Abelian Difference Sets; R.A. Liebler. Survey of Results on Signal Patterns for Locating One or Multiple Targets; O. Moreno. Sequence Design for CDMA Systems - Mean-Square Correlation Properties of Sequence Families; H.D. Schotten. Bent Functions and Coding Theory; J. Wolfmann. Recent Results on Difference Sets with Classical Parameters; Q. Xiang. Index.
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