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Ae-matrix algorithms associated frequency coefficients Aut(G automorphism group b-set bijection binary vectors bipartite graph bit nodes Chapter codewords columns comb complete graph compute constraint equations core Definition diagonal entries diagonalizable dimension edge in relation edge vector(space edge-to-edge adjacency matrix edges ek edges incident edges labelled eigen eigenvalues of HTH eigenvector Error-Correcting Codes example exists a permutation fact(n Figure graph is 1-transitive Group Theory H-matrix identity matrix incidence matrix Invariants ith associates Johnson association scheme l;b;p)-set code graph lexicographically ordered linear code linear programming problem maps minimum distance N.J.A. Sloane null matrix number of edges number of paths o o o p-set parity nodes possible 4-tuples Proof Qi(t reduced graph Reed-Muller Codes relation vectors set code 4-tuple set of relations temp Theorem thesis third components tion total graph associated transforms an edge tuples Vandermonde matrix vertex set