The functions DiscreteHadamardTransform,

InverseDiscreteHadamardTransform, and

HadamardMatrix take an option that changes the ordering of the rows and columns of the matrix.

The *i*th bit of a binary representation of an integer may be obtained using IntegerDigits. The sum defines an inner product of two vectors of length

m, whose elements are the binary digits of the

m-bit binary representations of the integers

*n* and

*k*.