I wrote,

[Wikipedia page on LFSR]

> It does not mention, for example, that one is calculating
> a remainder. I do not know anyone who uses the terminology
> Fibonacci LFSR, and the polynomial in the "Fibonacci" section
> is reversed from any normal usage.

A little more investigation and I have found other references
to the Fibonacci vs. Galois terminology distinction, including
in one paper by professor David Wagner at U.C. Berkeley.
So I guess it's a real bit of terminology.

In Golomb, _Shift Register Sequences_, Chapter 3 Section 2.8,
there is a discussion of how the polynomial P = 1 - x - x^2
generates a Fibonacci sequence (e.g., 1/P is an infinite
polynomial with Fibonacci numbers as coefficients). But
in a field of characteristic 2 this reduces to a sequence
of length three (every third Fibonacci number is even, the
others odd). So I do not immediately see how this leads to
the above Fibonacci nomenclature.

Steve