Vol. 85, No. 1, 1979

Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
Symmetric shift registers

Jan Søreng

Vol. 85 (1979), No. 1, 201–229
Abstract

We will study symmetric shift registers over the field GF(2) = {0,1}. The symmetric shift register 𝜃s : {0,1}n →{0,1}n corresponding to a symmetric polynomial S(x2,,xn) is defined by

𝜃S(a1,⋅⋅⋅ ,an) = (a2,⋅⋅⋅ ,an+1) where an+1 = a1 + S (a2,⋅⋅⋅ ,an).

p is a period of A ∈{0,1}n with respect to 𝜃s if 𝜃sP(A) = A. If p is the least period of A, then A 𝜃s(A) 𝜃SP(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 ∈{0,1}n.
  2. The possible minimal periods.
  3. The number of cycles corresponding to each minimal period.

Mathematical Subject Classification
Primary: 68D15, 68D15
Milestones
Received: 14 December 1977
Revised: 19 September 1978
Published: 1 November 1979
Authors
Jan Søreng