nx_fec_gf256.nx

nx_fec_gf256.nx -- the FEC CEILING: Reed-Solomon erasure coding over GF(256). MDS (maximum-distance-separable): an RS(n=K+R, K) code recovers ANY R lost symbols, in ANY positions -- not just the specific patterns XOR parity handles. This is the DSN/CCSDS/RaptorQ-class rateless recovery ceiling. Sovereign, integer-only: GF(256) tables are BUILT AT RUNTIME from the primitive polynomial 0x11D (sidesteps the const-array-literal gap, same trick as nx_crc32c), and a CAUCHY parity matrix guarantees every K x K submatrix is invertible (true MDS). Encoding matrix = [ I_K ; C ] where C[j][i] = 1 / ((K+j) ^ i) in GF(256) (disjoint Cauchy point sets -> non-singular). Decode: take the K rows for any K surviving symbols -> K x K matrix M -> data = M^-1 * survivors (Gauss-Jordan over GF(256)). Reconstructs every erased symbol. license_tier: ORIGINAL