On Jul 6, 8:12*am, spop...@speedymail.org (Steve Pope) wrote:

>
> (Is it not still true that each m-tuple represents a field element,
> in some basis?)

Yes, in a Galois LFSR, the m-tuple represents a field element
in the standard polynomial basis. If the initial loading of the
LFSR is 100....0 or 00....1 (depending on whether you are a
big-endian or a little-endian) representing the field element 1
(multiplicative identity), then successive m-tuple contents of
the Galois LFSR are alpha, alpha^2, alpha^3, .... or, for those
who dislike the Greek alphabet, x, x^2, x^3, etc, all modulo
the characteristic polynomial. The contents of the Fibonacci
LFSR are also the same sequence of increasing powers of
alpha, but the field elements are represented in the dual basis
of the standard polynomial basis. For further details, read
the thread from 7 years ago that has been cited earlier.

--Dilip Sarwate