On the counting function of the lattice profile of periodic sequences |
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| Authors: | Fang-Wei Fu Harald Niederreiter |
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| Affiliation: | aTemasek Laboratories, National University of Singapore, 5 Sports Drive 2, Singapore 117508, Republic of Singapore;bDepartment of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Republic of Singapore |
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| Abstract: | The lattice profile analyzes the intrinsic structure of pseudorandom number sequences with applications in Monte Carlo methods and cryptology. In this paper, using the discrete Fourier transform for periodic sequences and the relation between the lattice profile and the linear complexity, we give general formulas for the expected value, variance, and counting function of the lattice profile of periodic sequences with fixed period. Moreover, we determine in a more explicit form the expected value, variance, and counting function of the lattice profile of periodic sequences for special values of the period. |
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| Keywords: | Periodic sequences Lattice profile Linear complexity Discrete Fourier transform Expected value Variance Counting function |
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