 The probability that formula_67 happens is exactly formula_11.Thus, in fact, "all" non-zero codewords of the Hadamard code have relative Hamming weight formula_11, and thus, its relative distance is formula_11.The relative distance of the "augmented" Hadamard code is formula_11 as well, but it no longer has the property that every non-zero codeword has weight exactly formula_11 since the all formula_73s vector formula_74 is a codeword of the augmented Hadamard code.