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LINEAR BLOCK CODES
THE ARITHMETIC OF GALOIS FIELDS
12 other sections not shown
addition alternant codes BCH code Berlekamp-Massey algorithm binary code block codes burst error called channel circuit code of blocklength code over GF(q codeword coefficients columns components compute conjugacy constraint length construct convolutional code correct cyclic code cyclic convolution decoding algorithm defined definition denoted designed distance elements of GF(q encoder erasures error pattern error-control codes error-locator polynomial Euclidean example field element field GF(q Figure Fourier transform frame Galois field GF(p GF(qm Goppa code GRM code Hamming code Hence information bits information symbols input integer inverse iterations linear code majority decoder minimal polynomial minimum distance modulo multiplication node nomial nonzero parity frequencies parity-check equations parity-check matrix permutation polynomial g(x prime polynomial primitive element Proof prove quadratic residue received word recursive Reed-Muller code Reed-Solomon code relatively prime ring satisfies sequence shift register shown in Fig spectrum subspace two-dimensional vector space weight