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A New Class of Balanced Near-Perfect Nonlinear Mappings and Its Application to Sequence Design.
- Source :
-
IEEE Transactions on Information Theory . Feb2013, Vol. 59 Issue 2, p1090-1097. 8p. - Publication Year :
- 2013
-
Abstract
- A mapping from \BBZN to \BBZM can be directly applied for the design of a sequence of period N with alphabet size M, where \BBZN denotes the ring of integers modulo N. The nonlinearity of such a mapping is closely related to the autocorrelation of the corresponding sequence. When M is a divisor of N, the sequence corresponding to a perfect nonlinear mapping has perfect autocorrelation, but it is not balanced. In this paper, we study balanced near-perfect nonlinear (NPN) mappings applicable for the design of sequence sets with low correlation. We first construct a new class of balanced NPN mappings from \BBZp^{2-p} to \BBZp for an odd prime p. We then present a general method to construct a frequency-hopping sequence (FHS) set from a nonlinear mapping. By applying it to the new class, we obtain a new optimal FHS set of period p^2-p with respect to the Peng–Fan bound, whose FHSs are balanced and optimal with respect to the Lempel–Greenberger bound. Moreover, we construct a low-correlation sequence set with size p, period p^2-p, and maximum correlation magnitude p from the new class of balanced NPN mappings, which is asymptotically optimal with respect to the Welch bound. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 59
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 84994207
- Full Text :
- https://doi.org/10.1109/TIT.2012.2224146