Algebraic Coding Theory |
Contents
STARRED SECTIONS MAY BE SKIPPED ON FIRST READING | 1 |
ARITHMETIC OPERATIONS MODULO AN IRREDUCIBLE | 21 |
PROBLEMS | 63 |
Copyright | |
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According to Theorem affine polynomial affine subspace B₁ binary BCH code binary codes binary polynomial block length bound channel errors check digits code of block code of length codewords codewords of weight coefficients column compute convolutional codes correct coset cyclic code cyclic shifts decoding algorithm defined designed distance divides encoder error locations error patterns error-correcting Euclid's algorithm example extended BCH code field element function GF(p GF(pm GF(q GF(qm given Hamming code Hamming weight immediate subordinate integers irreducible binary irreducible factors irreducible polynomial Lee metric Lemma linear code minimal polynomial minimum distance multiple nomial nonzero nth root original code parity parity-check matrix permutation polynomial of degree prime primitive Proof q-ary QR code quadratic received word reciprocal roots RM code root of unity rows S₁ sequence subcode vector weight enumerator zero Σ Σ