On the Cross-Correlation Distributions of M-ary Multiplicative Character Sequences
SCIE
SCOPUS
- Title
- On the Cross-Correlation Distributions of M-ary Multiplicative Character Sequences
- Authors
- Han, YK; Yang, K
- Date Issued
- 2009-05
- Publisher
- IEEE-INST ELECTRICAL ELECTRONICS ENGI
- Abstract
- It is well known that the magnitude of the cross correlation between any distinct constant multiple sequences of an M-ary power residue sequence of period p is upper bounded by root p + 2 and that of an M-ary Sidel'nikov sequence of period p(m) - 1 is upper bounded by root p(m) + 3, where p is a prime and m, is a positive integer. In this paper, we first show that their cross-correlation functions are closely related to Jacobi sums and cyclotomic numbers. We then derive the cross-correlation distribution of constant multiple sequences of an M-ary power residue sequence. In the case of constant multiple sequences of an M-ary Sidel'nikov sequence, we get the possible cross-correlation values whose occurrence numbers are expressed in terms of the cyclotomic numbers of order M and are possibly zero.
- Keywords
- Cross correlation; cyclotomic numbers; Jacobi sum; multiplicative characters; power residue sequences; Sidel' nikov sequences; SIDELNIKOV SEQUENCES; PRIME
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/28822
- DOI
- 10.1109/TIT.2009.2016032
- ISSN
- 0018-9448
- Article Type
- Article
- Citation
- IEEE TRANSACTIONS ON INFORMATION THEORY, vol. 55, no. 5, page. 2384 - 2391, 2009-05
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