Title: Cyclic double struck capital F_q-linear double struck capital F_q^t-codes

Authors: W. Cary Huffman

Addresses: Department of Mathematics and Statistics, Loyola University of Chicago, Chicago, IL 60660, USA

Abstract: 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 F_q-linear double struck capital F_{q^t-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.}

Keywords: additive cyclic codes; quantum codes; self-orthogonal codes; error-correcting codes; additive codes.

DOI: 10.1504/IJICOT.2010.032543

International Journal of Information and Coding Theory, 2010 Vol.1 No.3, pp.249 - 284

Published online: 06 Apr 2010 *

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