Further results on the distinctness of decimations of l-sequences
Let (a) under bar be an l-sequence generated by a feedback-with-carry shift register with connection integer p(e), where p is an odd prime and e >= 1. Goresky and Klapper conjectured that when p(e) is not an element of {5, 9, 11, 13}, all decimations of (a) under bar 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 e >= 2 and p(e) not equal 9, all decimations of (a) under bar are also cyclically distinct.
l-sequences feedback-with-carry shift register (fcsr) arithmetic correlations 2-adic numbers integer residue ring primitive sequences