A Characterization of the q-Ary Images of q^m-Ary Cyclic Codes

Abstract

We give a simple characterization of the q-ary images of the q^m-ary cyclic codes of length n in the special case when the order of q module (q^m − 1)/(n,q^m − 1) is m. This is done by introducing an appropriate modulo structure on F ^mn _q .

Part of the work reported in this paper was done in the summer of 1991 while the first author was at the Université de Toulon, FRANCE, supported by a research fellowship from the French government. This work was also partly funded by research grant number 0GP00G288 from the Natural Sciences and Engineering Research Council of Canada, held by the first author at the Ecole Polytechnique de Montréal.