The Distributing Regulation of the Shortest Linear Recurring Length over the Finite Field
Luo Yun · Chinese Journal of Computers · 2005
In this paper,when B-M algorithm is applied to search the shortest linear recurring length of single sequence over the finite field F(q),the distribution of the shortest linear recurring sequence over the finite field F(q) is studied.The amount of the sequences,whose length is n and shortest linear recurring length is l,has been calculated where 0ln.It is found that the shortest linear recurring length l is always equal to n/2 or n/2+1 for any sequence of length n.In other words,it is always equal to the half of the length of the given sequence.