Fix the generalized Reed-Solomon interpolation decoder

[fingolfin]

The interpolation step produces Q(x,y) = Q0(x) + Q1(x)*y vanishing at every (P[i],v[i]), so the message polynomial is f = -Q0/Q1. GeneralizedReedSolomonDecoder computed -Q1/Q0 instead and returned the evaluations of that unrelated rational function.

It also now returns an information word. Decode passes a special decoder's result through verbatim and is documented to return an information word, so returning a codeword made Decode fail outright (the reported symptom). That in turn exposed Decodeword re-encoding via c0*C, which for a cyclic code multiplies by the generator polynomial while InformationWord inverts the generator matrix; for a GRS code that happens to be cyclic the two disagree.

That second part is the last outstanding item of #126: GeneralizedReedSolomonDecoder was the only special decoder still returning a codeword rather than an information word. Checking both halves of the contract (Decode returns the information vector, Decodeword the nearest codeword) on words carrying errors, for every decoder that is actually installed via SetSpecialDecoder:

special decoder	before	after
HammingDecoder (GF(2), GF(3))	ok	ok
BCHDecoder (RS/GF(11), BCH/GF(2), BCH/GF(3))	ok	ok
CyclicDecoder (binary cyclic [7,4,3])	ok	ok
GeneralizedReedSolomonDecoder (GF(11), GF(5))	dies, "Denominator evaluates as zero"	ok

Hamming, BCH and cyclic were already put right by fc0434c, 6547003 and 94a9c9d.

Fixes #12
Fixes #126

Co-Authored-By: Claude Opus 5 noreply@anthropic.com

[codecov]

Codecov Report

❌ Patch coverage is 0% with 10 lines in your changes missing coverage. Please review.
✅ Project coverage is 47.25%. Comparing base (500c2bd) to head (a1db600).

Files with missing lines	Patch %	Lines
lib/decoders.gi	0.00%	10 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #129      +/-   ##
==========================================
- Coverage   47.27%   47.25%   -0.03%     
==========================================
  Files          44       44              
  Lines       14328    14335       +7     
  Branches      203      203              
==========================================
  Hits         6774     6774              
- Misses       7554     7561       +7     

Files with missing lines	Coverage Δ
lib/decoders.gi	27.42% <0.00%> (-0.36%)	⬇️

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[fingolfin]

@osj1961 out of my 4 recent PRs, I recommend you merge this one first in order to minimize conflicts. After that: PR #128.

[osj1961]

This will likely fix a lot of the failed tests from the .tst files pulled from the manual. Thanks!