55 lines
1.1 KiB
C++
55 lines
1.1 KiB
C++
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#include "decoding.h"
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bool syndrome_decode (bvector&syndrome, gf2m&fld, polynomial& goppa,
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std::vector<polynomial>& sqInv, bvector&ev,
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bool check_failure)
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{
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ev.clear();
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ev.resize (fld.n, 0);
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if (syndrome.zero() ) return true;
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polynomial v;
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syndrome.to_poly (v, fld);
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v.inv (goppa, fld); // v=Synd^-1 mod goppa
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if (v.size() < 2) v.resize (2, 0);
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v[1] = fld.add (1, v[1]); //add x
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v.sqrt (sqInv, fld); //v = sqrt((1/s)+x) mod goppa
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polynomial a, b;
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v.mod_to_fracton (a, b, goppa, fld);
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a.square (fld);
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b.square (fld);
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b.shift (1);
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a.add (b, fld); //new a = a^2 + x b^2
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a.make_monic (fld); //now it is the error locator.
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for (uint i = 0; i < fld.n; ++i) {
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if (a.eval (i, fld) == 0) {
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ev[i] = 1;
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if (!check_failure) continue;
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//check if the error locator splits over GF(2^m).
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//We simplify it to the assumption that all roots are
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//also roots of linear factors.
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polynomial t, q, r;
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t.resize (2, 0);
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t[0] = i;
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t[1] = 1;
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a.divmod (t, q, r, fld);
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if (r.degree() >= 0) {
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ev.clear();
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return false;
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}
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a = q;
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}
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}
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return true;
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}
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