Comments on "A Note on Perfect Arithmetic Codes"
IEEE Transactions on Information Theory, Vol. IT-34, pp. 589-590, May 1988.
Antoine LOBSTEIN
Centre National de la Recherche Scientifique
Ecole Nationale Supérieure des Télécommunications
46 rue Barrault, 75634 Paris cédex 13, France
Abstract.Two definitions of modular distance relative to modulus M>0 and radix r>1 are known. Recently, Astola has constructed new binary perfect arithmetic codes, considering the modular distance introduced by Rao and Garcia. However, if we consider the modular distance defined by Clark and Liang, these codes are not perfect any more. This fact can be generalized somewhat.