Further Results on the Distinctness of Decimations of l-sequences

Abstract

Let $\underline{a}$ be an \textit{l}-sequence generated by a feedback-with-carry shift register with connection integer $q=p^e$, where $p$ is an odd prime and $e\ge 1$. Goresky and Klapper conjectured that when $p^e\notin \{5,9,11,13\}$, all decimations of $\underline{a}$ 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 $e\ge 2$ and$p^e\ne 9$, all decimations of $\underline{a}$ are also cyclically distinct.

submitted to IEEE-IT