Lecture Notes in Computer Science, No. 539, pp. 246-258, Springer-Verlag, 1991.
Antoine LOBSTEIN & Patrick SOLÉ
Centre National de la Recherche Scientifique
Abstract. Arithmetic codes are used to check or correct arithmetic operations on computers, such as addition or modular addition, on integers which are represented in a fixed radix r (r > 1). The need for a measure of an error leads one to define the weight of an integer. Three definitions are known (one of them does not always satisfy the triangle inequality). From these notions, several problems arise (for instance, about perfect codes). We list these problems together with complete or partial previously known results, as well as some new results.