In Calderbank, self-orthogonal additive codes over double struck capital F4 under the traceinner product were connected to binary quantum codes; a similar connection was given in the non-binary case in Rains. In this paper, we consider a natural generalisation of additive codes to double struck capital Fq-linear double struck capital Fqt-codes. We develop the theory of these codes when they are cyclic and count them. Then, we place two different trace inner products on these codes and decide precisely when the cyclic ones are self-orthogonal under these two inner products. We examine the case t = 2 in detail giving specific bases for the self-orthogonal and self-dual cyclic codes. When t ≥ 2, we present counts for the number of self-orthogonal and self-dual cyclic codes under each of the inner products.
['W. Cary Huffman']
Cyclic double struck capital Fq-linear double struck capital Fqt-codes