TY - JOUR
AU - Yogesh Kumar
AU - N.R. Pillai
AU - R.K. Sharma
PY - 2016/10/31
Y2 - 2022/08/17
TI - On the Number of Integer Recurrence Relations
JF - Defence Science Journal
JA - DSJ
VL - 66
IS - 6
SE - Special Issue Papers
DO - 10.14429/dsj.66.10801
UR - https://publications.drdo.gov.in/ojs/index.php/dsj/article/view/10801
AB - This paper presents the number of k-stage integer recurrence relations (IRR) over the ring Z2 which generates sequences of maximum possible period (2k-1)2e-1 for e>1. This number corresponds to the primitive polynomials mod 2 which satisfy the condition proposed by Brent and is2(e-2)k+1(2k-1-1) for e>3. This number is same as measured by Dai but arrived at with a different condition for maximum period. Our way of counting gives an explicit method for construction of such polynomials. Furthermore, this paper also presents the number of different sequences corresponding to such IRRs of maximum period.
ER -