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The number of nonlinear shift registers that produce all vectors of weight ⩽t

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1 Author(s)
H. Fredricksen ; Dept. of Math., US Naval Postgraduate Sch., Monterey, CA, USA

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

Published in:

IEEE Transactions on Information Theory  (Volume:39 ,  Issue: 6 )