New construction for binary sequences of period p(m)-1 with optimal autocorrelation using (z+1)(d)+az(d)+b
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- Title
- New construction for binary sequences of period p(m)-1 with optimal autocorrelation using (z+1)(d)+az(d)+b
- Authors
- No, JS; Chung, H; Song, HY; Yang, K; Lee, JD; Helleseth, T
- Date Issued
- 2001-05
- Publisher
- IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
- Abstract
- In this correspondence, we present a construction for binary sequences {s(t)} of period N = p(m) - 1 for an odd prime p based on the polynomial (z + 1)(d) + az(d) + b, and discuss them in some cases of parameters p, m, d, a, and b. We show that new sequences from our construction are balanced or almost balanced and have optimal three-level autocorrelation for the case when the polynomial (z + 1)(d) + z(d) + a can be transformed into the form m(2) - c. We also derive the distribution of autocorrelation values they take on. The sequences satisfy constant-on-the-coset property, and we will show that there are more than one characteristic phases with constant-on-the-coset property. Some other interesting properties of these sequences will be presented. For the cases when the polynomial (r + 1)(d) + z(d) + a cannot be transformed into the form z(2) - c, we performed extensive computer search, and results are summarized. Based on these results, some open problems are formulated.
- Keywords
- cyclotomic numbers; optimal autocorrelation; pseudorandom sequences; randomness properties; PSEUDORANDOM SEQUENCES; IDEAL AUTOCORRELATION; GMW SEQUENCES
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/19535
- ISSN
- 0018-9448
- Article Type
- Article
- Citation
- IEEE TRANSACTIONS ON INFORMATION THEORY, vol. 47, no. 4, page. 1638 - 1644, 2001-05
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