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Weight enumerators of codes
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affine space algebraic association scheme Assume base point binary block designs BOSE called chapter code of order coding theory compatible condition configuration contains defined definition DEMBOWSKI denote diagonal distance elements example exists field F finite nearaffine space following theorem fully indecomposable Gauss sum geometries GF(q given Gleason's theorem graph Hamming schemes Hence hyperplane implies incidence matrix ind(x indeterminates invariants of G Johnson schemes lemma Let F line G linear codes MACWILLIAMS Math matrix equation metric scheme Molien series N.J.A. Sloane nearfield nearly perfect codes non-zero number of points obtain orthogonal Latin squares pairwise perfect codes permutation groups polynomial positive integers prime power projective plane PROOF properties proposition 2.2 prove Q-polynomial quadratic residue quasigroups remark root of unity self-dual code straight lines subset theorem 3.2 transversal design vector weight enumerator x,y e zero