Paper Info
Title
Trace Representation And Linear Complexity Of Binary Eth Power Residue Sequences Of Period P
Abstract
Let p = ef + 1 be an odd prime for some e and f, and let F(p) be the finite field with elements. In this paper, we explicitly describe the trace representations of the binary characteristic sequences (of period p) of all the cyclic difference sets D which are some union of cosets of eth powers H(e) in F(p)* (Delta F(p)\{0} for e <= 12. For this, we define eth power residue sequences of period p, which include all the binary characteristic sequences mentioned above as special cases, and reduce the problem of determining their trace representations to that of determining the values of the generating polynomials of cosets of H(e) in F(p)* at some primitive pth root of unity, and some properties of these values are investigated. Based on these properties, the trace representation and linear complexity not only of the characteristic sequences of all the known eth residue difference sets, but of all the sixth power residue sequences are determined. Furthermore, we have determined the linear complexity of a nonconstant eth power residue sequence for any e to be either p - 1 or p whenever (e, (p - 1)/n) = 1, where n is the order of 2 mod p.
Year
DOI
Venue
2011
10.1109/TIT.2010.2103757
IEEE TRANSACTIONS ON INFORMATION THEORY
Keywords
DocType
Volume
Binary sequences with two-level autocorrelation, cyclic difference sets, eth residue cyclic difference sets, linear complexity, minimal polynomials, trace representations
Journal
57
Issue
ISSN
Citations 
3
0018-9448
0
PageRank 
References 
Authors
0.34
0
4
Name
Order
Citations
PageRank
Zong-duo Dai120325.53
Guang Gong21717160.71
Hong-Yeop Song332951.84
Dingfeng Ye4547.67