ON THE THEORY OF Fq-LINEAR Fqt-CODES

In [7], self-orthogonal additive codes over F-4 under the trace inner product were connected to binary quantum codes; a similar connection was given in the nonbinary case in [33]. In this paper we consider a natural generalization of additive codes called F-q-linear F-qt-codes. We examine a number of classical results from the theory of F-q-linear codes, and see how they must be modified to give analogous results for F-q-linear F-qt-codes. Included in the topics examined are the MacWilliams Identities, the Gleason polynomials, the Gleason-Pierce Theorem, Mass Formulas, the Balance Principle, the Singleton Bound, and MDS codes. We also classify certain of these codes for small lengths using the theory developed.