Further Results on the Distinctness of Decimations of$l$-Sequences
H. Xu, Wuqiang Qi · IEEE Transactions on Information Theory · 2006
Let$underlinea$be an l-sequence generated by a feedback-with-carry shift register with connection integer$p^e$, where$p$is an odd prime and$egeq 1$. Goresky and Klapper conjectured that when$p^enotin 5,9,11,13$, 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 decimations are distinct. In this article, we further show that when$egeq 2$and$p^eneq 9$, all decimations of$underlinea$are also cyclically distinct.