A New Class of Balanced Near-Perfect Nonlinear Mappings and Its Application to Sequence Design
SCIE
SCOPUS
- Title
- A New Class of Balanced Near-Perfect Nonlinear Mappings and Its Application to Sequence Design
- Authors
- Chung, JH; Yang, K
- Date Issued
- 2013-02
- Publisher
- IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
- Abstract
- A mapping from Z(N) to Z(M) can be directly applied for the design of a sequence of period with alphabet size, where Z(N) denotes the ring of integers modulo. The nonlinearity of such a mapping is closely related to the autocorrelation of the corresponding sequence. When is a divisor of, 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 Z(p2-p) to Z(p) 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.
- Keywords
- Balancedness; frequency-hopping sequences (FHS); Hamming correlation; nonlinear mappings; periodic correlation; FREQUENCY-HOPPING SEQUENCES; PERIODIC CORRELATION-PROPERTIES; LARGE LINEAR SPAN; CROSS-CORRELATION; SIDELNIKOV SEQUENCES; OPTIMAL CONSTRUCTIONS; ARY SEQUENCES; LOWER BOUNDS; FAMILIES; SETS
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/15723
- DOI
- 10.1109/TIT.2012.2224146
- ISSN
- 0018-9448
- Article Type
- Article
- Citation
- IEEE TRANSACTIONS ON INFORMATION THEORY, vol. 59, no. 2, page. 1090 - 1097, 2013-02
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