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Finite Fields and Coding Theory
Combinatorial Constructions and Coding
Coding and Combinatorics
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algebra basis BCH code BIBD binary code bound chain group chapter code of length code over GF(q code vectors codeword coding theory coefficients column consider construction coordinate positions Corollary cyclic code defined Definition dendroid denote dimension distinct EG(m EG(n elements of GF(q equation equidistant code equivalent exists finite fields flat in PG(n GF(p GF(qm Golay code GRM code Hadamard matrix hence implies incidence matrix incidence vectors irreducible polynomial Lemma length pms linear code MacWilliams majority logic decodable matrix H matroid minimal polynomial minimum distance minimum weight nomial obtained parameters parity check matrix PG(m plane of order points polynomial code polynomial of degree positive integer prime primitive element projective geometry projective geometry code projective plane Proof Let quadratic residue root of unity self-dual codes splitting field Steiner system subfield subset subspace Suppose symmetric tuples vector space weight enumerator zero