Re: Announcing cdrskin-0.7.2
| From: Thomas Schmitt <scdbackup@gmx.net>
| 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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