On Normal and Subnormal q-ary Codes
IEEE Transactions on Information Theory, Vol. IT-35, pp. 1291-1295, November 1989.
Antoine LOBSTEIN
Centre National de la Recherche Scientifique
Ecole Nationale Supérieure des Télécommunications
46 rue Barrault, 75634 Paris cédex 13, France
& G.J.M. VAN WEE
Department of Mathematics and Computer Science
Eindhoven University of Technology
P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Abstract. We extend to the q-ary case the notions of a normal code, a subnormal code, and the amalgamated direct sum comstruction. These concepts were defined in the binary case to investigate problems related to the covering radius of codes. Many nonbinary covering codes appear to be absubnormal. In particular, we prove that every nonbinary nontrivial perfect code is absubnormal. We also include some linear programming lower bounds on ternary codes with covering radii 2 or 3.