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test: Reed-Solomon cannot see that the derandomiser was skipped - #4
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The pipeline is sync, derandomise, Reed-Solomon, and the ordering has been wrong in this repository's own prose once already. The reason it matters is not obvious and is now a test rather than a sentence. RS(255,223) is linear over GF(2^8), so the sum of two codewords is a codeword, and over GF(2) that sum is XOR. The 255-octet randomiser sequence of CCSDS 131.0-B-5 10.4 is itself a codeword. A randomised frame is therefore `codeword XOR sequence` — a codeword, exactly, with zero syndromes. So a block that has not been derandomised decodes clean, reports zero corrections, and disagrees with the frame it came from in all 255 of its 255 symbols. The error-correcting code is blind to the one mistake somebody reordering this pipeline would make. The test asserts all three: the sequence decodes as a codeword, arbitrary bytes of the same length do not, and a randomised real frame comes back Ok(0) and wrong everywhere.
E=16 and E=32 take consecutive roots from the same generator, so RS(255,223) is a subcode of RS(255,239) and the trap holds for both. Asserted rather than reasoned about, and the frame length now comes from the code instead of being 223 twice.
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The pipeline is
synchronise → derandomise → Reed-Solomon, and this repository's ownARCHITECTURE.md had that order backwards once already. Why it matters is not obvious, so it
is a test now instead of a sentence.
RS(255,223) is linear over GF(2⁸): the sum of two codewords is a codeword, and over GF(2) that
sum is XOR. The 255-octet randomiser sequence of CCSDS 131.0-B-5 §10.4 turns out to be a
codeword itself. A randomised frame is therefore
codeword XOR sequence— which is acodeword, exactly, with zero syndromes.
So a block nobody derandomised decodes clean:
The error-correcting code is blind to the one mistake somebody reordering this pipeline would
make. There is no diagnostic to add; the order is the whole defence.
The test asserts all three legs: the sequence decodes as a codeword, arbitrary bytes of the
same length do not (so the first leg is not vacuous), and a real encoded frame that was
randomised comes back
Ok(0)and wrong in every symbol.532 tests, fmt and clippy clean.