A Simple Method for Obtaining Primitive Pentanomials Over GF (2)
Hiroshi Kashiwagi, Tetsuya UCHIMURA · Transactions of the Society of Instrument and Control Engineers · 1982
A new and simple method is described for obtaining several primitive pentanomials over GF (2) from primitive trinomials of the same order.It is shown that for a given n-th order primitive trinomialf(x)=xn+xp+1we can easily obtain some of the primitive pentanomials of n-th order, if there exists an integer r such that for s=2m+1 (m: integer), (1) p=rs or (2) n=rs or (3) n-p=rs.All the primitive pentanomials of up to 1, 000 degree obtained by this method are shown in the table.