2006/01/09 by Hong Xu, Xu, Hong, Wen-Feng Qi +1
Computer Science · #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #cs.CR
paper · pdf · doi:10.48550/arxiv.cs/0601024
submitted to IEEE-IT
arxiv created 2006/01/09 · arxiv updated 2009/12/01
Let \underlinea be an l-sequence generated by a feedback-with-carry shift register with connection integer q=pe, where p is an odd prime and e≥ 1. Goresky and Klapper conjectured that when pe∉ \5,9,11,13\, all decimations of \underlinea are cyclically distinct. When e=1 and p>13, they showed that the set of distinct decimations is large and, in some cases, all deciamtions are distinct. In this article, we further show that when e≥ 2 and pe≠ 9, all decimations of \underlinea are also cyclically distinct.