Figure 2

Walsh functions. The first 32 Paley-ordered Walsh functions \(\operatorname {PAL}_{k}\), \(k\in\{ 0,\ldots,31\}\). Functions with maximum Hamming weight \(r(k)\) (hence maximum number of Rademacher functions) for given \(m(k)\), corresponding to Paley orders \(2^{m(k)}-1\), are highlighted in red.