Other Constructions of H _n

Abstract

Ahmed and Rao (1975) provide an exponential definition for H _n by writing it directly as

$$ \begin{gathered} {H_n} = ({h_{{i,j}}}) \hfill \\ \quad = {( - 1)^{{\left\langle {i,j} \right\rangle }}} \hfill \\ \end{gathered} $$

(55)

where 〈i, j〉 is the modulo-two inner product of the two normal binary representations of i and j. Table 1 shows calculation of the inner product for H ₂ .