Simple coding scheme for modular arithmetic

Most implementations of modular arithmetic are restricted to the cases M = 2 to the n power - 1 or M = 2 to the n power plus 1 since arithmetic modulo numbers of this form are straightforward and the computation of transforms can be made multiplication-free. It is pointed out, however, that if M is allowed to take on more complex forms, the number of transform points can be increased for the same word length (Dubois and Venetsanopoulos, 1978; Pollard, 1976). The scheme presented here is a dual representation scheme that allows for easy encoding of numbers and avoids the problem of checking for unused combinations. The coding scheme maps each integer N, which is in the range of values less than M and greater than or equal to 0, into one of two representations; each is identified by its most significant bit. With this scheme, the encoding of numbers is straightforward and the problem of checking for unused combinations is eliminated