Symmetric shift registers
Jan Søreng · Pacific Journal of Mathematics · 1979
JAN SΘRENGWe will study symmetric shift registers over the field GF( 2) = {0,1}.The symmetric shift register Θ s : {0, l} n -> {0, l} n corresponding to a symmetric polynomial S(x 2 , •••,#") is defined by Θ S (QΊ, •••,»«) = (tt2> * *> α»n) where α n+1 = α x + S(α 2 , , α n ) .ί> is a period of ^4 e {0, I} 71 with respect to # Θ S (A) ->...-> 0J(A) = -A is the cycle corresponding to A.This is the first of two papers where we will determine in a constructive way (for each S):1.The minimal period for each A e {0, I} 71 .2. The possible minimal periods.3. The number of cycles corresponding to each minimal period.204 JAN S0RENG (3.3) t G D means t e [l(D\ r(D)] .