An nxn matrix with entries either 1 or -1 where each row is orthogonal to every other row. Of course, a row's inner product with itself is n. So when you multiply a Hadamard matrix times it's transpose you get n times the identity matrix.
A chain in a graph such that the nodes of the chain comprise all the nodes of the graph.
A cycle in a graph such that the nodes of the cycle comprise all the nodes of the graph.
In a binary code a distance can be defined between code words, given two words v and w the Hamming distance, d(v,w) is the number of positions in which they differ.
0100110110111 and 0010110110111are at Hamming distance 2 from one another.
A graph obtained from another by inserting new nodes along existing edges. The following graph is a homeomorph of K(5) .
A regular polytope, the convex hull of the points (e1,...,ed) where each coordinate ei is either 0 or 1.
A (d-1)-dimensional flat in Rd.