[email protected] <[email protected]> wrote:

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

[Fibonacci LFSR]

>> (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.

Thanks. I read through the cited thread.

I assume this is perhaps the same dual basis that Berlekamp used
to develop his bit-serial RS encoder.

I am still curious about the origin and dissemination of the
"Fibonacci LFSR" vs. "Galois LFSR" terminology -- there isn't
anything less "Galois" about the Fibonacci version; it uses a
different basis, sure, but the register contents are still Galois
field elements. So I see it as a confusing choice of terms for
this distinction.

Unless this terminology is really and truly ingrained,
I'd advocate spiking it.

Just my opinion of course.

Steve