A New Family of p-Ary Sequences of Period (p(n)-1)/2 With Low Correlation
- Authors
- Kim, Ji-Youp; Choi, Sung-Tai; No, Jong-Seon; Chung, Habong
- Issue Date
- Jun-2011
- Publisher
- IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
- Keywords
- Autocorrelation; characters; cross-correlation; finite fields; Kloosterman sums; nonbinary sequences
- Citation
- IEEE TRANSACTIONS ON INFORMATION THEORY, v.57, no.6, pp.3825 - 3830
- Journal Title
- IEEE TRANSACTIONS ON INFORMATION THEORY
- Volume
- 57
- Number
- 6
- Start Page
- 3825
- End Page
- 3830
- URI
- https://scholarworks.bwise.kr/hongik/handle/2020.sw.hongik/19870
- DOI
- 10.1109/TIT.2011.2133730
- ISSN
- 0018-9448
- Abstract
- For an odd prime p congruent to 3 modulo 4 and an odd integer n, a new family of p-ary sequences of period N = p(n)-1/2 with low correlation is proposed. The family is constructed by shifts and additions of two decimated m-sequences with the decimation factors 2 and 2d, d = N - p(n-1). The upper bound for the maximum magnitude of nontrivial correlations of this family is derived using well known Kloosterman sums. The upper bound is shown to be 2 root N + 1/2 = root 2p(n), which is twice the Welch's lower bound and approximately 1.5 times the Sidelnikov's lower bound. The size of the family is 2(p(n) - 1), which is four times the period of sequences.
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