2016/02/18 by Şaban Alaca, Alaca, Şaban, Goldwyn Millar +1
Computer Science · Mathematics · #05B10 #11B50 #11T23 #11T71 #94A55 #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Number Theory (math.NT) #cs.IT #math.CO #math.IT #math.NT #msc:05B10 #msc:11B50 #msc:11T23 #msc:11T71 #msc:94A55
paper · pdf · doi:10.48550/arxiv.1602.05888
arxiv created 2016/02/18 · arxiv updated 2016/02/19
Binary sequences with good autocorrelation properties and large linear complexity are useful in stream cipher cryptography. The Sidelnikov-Lempel-Cohn-Eastman (SLCE) sequences have nearly optimal autocorrelation. However, the problem of determining the linear complexity of the SLCE sequences is still open. Our approach is to exploit the fact that character values associated with the SLCE sequences can be expressed in terms of a certain type of Jacobi sum. By making use of known evaluations of Gauss and Jacobi sums in the "pure" and "small index" cases, we are able to obtain new insight into the linear complexity of the SLCE sequences.