On Perfect Binary Arithmetic Codes which can Correct two Errors or more
Ars Combinatoria, Vol. 29, pp. 24-27, June 1990.
Antoine LOBSTEIN
Centre National de la Recherche Scientifique
Ecole Nationale Supérieure des Télécommunications
46 rue Barrault, 75634 Paris cédex 13, France
Abstract. We state here that, for modulus modd and less than 229+227-1, no (nontrivial) perfect binary arithmetic code, correcting two errors or more, exists (this is to be taken with respect to the Garcia-Rao modular distance). In particular, in the case m= 2n+1 or 2n-1, which is most frequently studied, no such code exists for m< 233-1.