Title :
The number of nonlinear shift registers that produce all vectors of weight ⩽t
Author :
Fredricksen, Harold
Author_Institution :
Dept. of Math., US Naval Postgraduate Sch., Monterey, CA, USA
fDate :
11/1/1993 12:00:00 AM
Abstract :
It has been shown that it is possible to generate a cycle on a nonlinear shift register to contain all vectors of length n and Hamming weight ⩽t. It is shown how to count the number of different ways this can be done on a truth table of minimum density. Specifically, it is shown how a theorem on spanning subtrees on a graph can be used to evaluate the number of sequences that contain vectors of a given length and Hamming weight
Keywords :
binary sequences; logic design; shift registers; trees (mathematics); Hamming weight; graph; nonlinear shift registers; sequences; spanning subtrees; truth table of minimum density; vector length; Binary sequences; Feedback; Hamming weight; Mathematics; Shift registers; Surgery; Tree graphs;
Journal_Title :
Information Theory, IEEE Transactions on
