Key Papers in the Development of Coding Theory

a₁ algebraic alphabet b₁ b₂ BCH codes Berlekamp binary digits binary symmetric channel block codes block length Bose-Chaudhuri branches C₁ channel symbols circuit code word coding theory coefficients columns constraint length construction convolutional codes correcting codes corresponding coset cyclic codes decoding algorithm decoding error decoding procedure defined denote elements equations equivalent erasure error probability error-correcting codes finite field follows function GF(q given Golay group codes Hamming Hence IEEE Trans information digits input integer invariant factors inverse Lemma linear linear code lower bound Math matrix minimal encoder minimum distance modulo multiple node nonzero number of computations obtained output P₁ parity check path perfect codes polynomial probability of error Proof received Reed-Muller code root S₁ satisfied sequence sequential decoding signal Theorem tion transmission transmitted tree vector weight distribution zero декодирования кодов операций число