Re: Announcing cdrskin-0.7.2

| From: Thomas Schmitt <[email protected]>
| Do you know by chance a smart student who can
| contribute an implementation or explanation of
| ECMA-130 Annex A ?
| 
| "The RSPC is a product code over GF(28) producing
|  P- and Q-parity bytes. The GF(28) field is
|  generated by the primitive polynomial
|  P(x) = x8 + x4 + x3 + x2 + 1
|  The primitive element a of GF(28) is
|  a = (00000010) where the right-most bit is the
|  least significant bit.
|  [...]
| "
| The words "RSPC" and "P- and Q-parity bytes"
| belong to the CD sector format specs. But the
| others must be established mathematic terms.
| (How is this connected to a Fourier
|  transformation of the bit sequence on time
|  domain ? Urgh ! Analysis ! On a finite set !)

I am not a mathematician.

I'd guess that this is really GF(2^8).  GF stands for Gallois Field.
Gallois Fields have size p^m where p is a prime (in our case, 2).

Ahh.  The standard confirms this:
  http://www.ecma-international.org/publications/files/ECMA-ST/Ecma-130.pdf

Thus all elements of GF(2^8) would be polynomials of degree 7 or less.
The coefficients are from the integers mod 2 and thus any polynomial
in this field can be represented as 8 bits.

The primitive polynomial would be:
P(x) = x^8 + x^4 + x^3 + x^2 + x^0

See http://en.wikipedia.org/wiki/Finite_field

RSPC seems to be Reed-Solomon Product-like Code.  See
  http://en.wikipedia.org/wiki/Finite_field

>From that article, it looks as if the discrete Fourier transform you
require can be done by a cook book method:
  http://en.wikipedia.org/wiki/Berlekamp-Massey_algorithm

I admit that I'm shooting from the hip here.  But it seems as if the
internet has enough information to get to a solution.


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