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1. left part of G is E, because we use Reed-Solomon algo; so left part of S @ G is S and cutting right colomns works; my_fix(G) returns E and in break_S we needn't get inv(G), just S = my_fix(G_ @ inv(P)), check it; try break_S with another (not Reed-Solomon) code (matrix G will be different; will my_fix(G) and my_fix(G_) return nonsingular matrices?; of course, rank(G) = rank(G_) = k and we can iterate through all possible combinations of column deletions and find one that does not lead to a nonsingular matrices); another way to get S is calculating it row by row (solving k systems, each has n equations with k variables, k < n, but we need to do it in Galois Field)
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1. left part of G is E, because we use Reed-Solomon algo; so left part of S @ G is S and cutting right colomns works; my_fix(G) returns E and in break_S we needn't get inv(G), just S = my_fix(G_ @ inv(P)), check it; try break_S with another (not Reed-Solomon) code (matrix G will be different; will my_fix(G) and my_fix(G_) return nonsingular matrices?; of course, rank(G) = rank(G_) = k and we can iterate through all possible combinations of column deletions and find one that does not lead to nonsingular matrices); another way to get S is calculating it row by row (solving k systems, each has n equations with k variables, k < n, but we need to do it in Galois Field)
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