مرکز منطقه ای اطلاع رساني علوم و فناوري - On the distribution of de Bruijn sequences of given complexity

DocumentCode :

939109

Title :

On the distribution of de Bruijn sequences of given complexity

Author :

Etzion, Tuvi ; Lempel, Abraham

Volume :

Issue :

fYear :

1984

fDate :

7/1/1984 12:00:00 AM

Firstpage :

611

Lastpage :

614

Abstract :

The distribution $\\gamma (c, n)$ of de Bruijn sequences of order $n$ and linear complexity $c$ is investigated. It is shown that for $n \\geq 4, \\gamma (2^{n} - 1, n) \\equiv 0 \\pmod {8}$ , and for $k \\geq 3, \\gamma (2^{2k} - 1,2k) \\equiv 0 \\pmod {l6}$ . It is also shown that $\\gamma (c, n) \\equiv 0 \\pmod {4}$ for all $c$ , and $n \\geq 3$ such that $cn$ is even.