Computer Science – Information Theory
Scientific paper
2009-12-02
Computer Science
Information Theory
This paper was submitted to the journal Theoretical Computer Science
Scientific paper
Let $S=(s_1,s_2,...,s_m,...)$ be a linear recurring sequence with terms in $GF(q^n)$ and $T$ be a linear transformation of $GF(q^n)$ over $GF(q)$. Denote $T(S)=(T(s_1),T(s_2),...,T(s_m),...)$. In this paper, we first present counter examples to show the main result in [A.M. Youssef and G. Gong, On linear complexity of sequences over $GF(2^n)$, Theoretical Computer Science, 352(2006), 288-292] is not correct in general since Lemma 3 in that paper is incorrect. Then, we determine the minimal polynomial of $T(S)$ if the canonical factorization of the minimal polynomial of $S$ without multiple roots is known and thus present the solution to the problem which was mainly considered in the above paper but incorrectly solved. Additionally, as a special case, we determine the minimal polynomial of $T(S)$ if the minimal polynomial of $S$ is primitive. Finally, we give an upper bound on the linear complexity of $T(S)$ when $T$ exhausts all possible linear transformations of $GF(q^n)$ over $GF(q)$. This bound is tight in some cases.
Fu Fang-Wei
Gao Zhi-Han
No associations
LandOfFree
The minimal polynomial of sequence obtained from componentwise linear transformation of linear recurring sequence does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The minimal polynomial of sequence obtained from componentwise linear transformation of linear recurring sequence, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The minimal polynomial of sequence obtained from componentwise linear transformation of linear recurring sequence will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-508202