A Simple Left-to-Right Algorithm for Minimal Weight Signed Radix-$r$ Representations

We present a simple algorithm for computing the arithmetic weight of an integer with respect to a given radix rges2. The arithmetic weight of n is the minimum number of nonzero digits in any signed radix-r representation of n. This algorithm leads to a new family of minimal weight signed radix-r representations which can be constructed using a left-to-right on-line algorithm. These representations are different from the ones previously discovered by Joye and Yen. The idea behind our algorithm is that of choosing closest elements which was introduced by Muir and Stinson. Our results have applications in coding theory and in the efficient implementation of public-key cryptography