Lecture Notes in Computer Science, No. 311, pp. 56-67, Springer-Verlag, 1988.
Antoine LOBSTEIN
Centre National de la Recherche Scientifique
Ecole Nationale Supérieure des Télécommunications
46 rue Barrault, 75634 Paris cédex 13, France
Abstract. Errors arising in addition modulo M in computer computations can be detected and corrected by arithmetic codes. To more adequately describe the weight of such errors, Garcia and Rao introduced the modular distance (relative to modulus M > 0 and radix r > 1) which, unfortunately, does not, in general, satisfy the triangular inequality (however, it does hold for the cases of greatest practical interest). To supply it, Clark and Liang gave a new definition of modular distance, which always satisfies the triangular inequality.
We investigate the problem of when these two definitions are identical.
Acknowledgment. This work was done during a three-month stay at the University of Technology of Eindhoven, and supported by a grant from this university.
I am very grateful to Professor van Lint, who provided me with a research fellowship, and received me in his Department.