Construction of self-dual matrix codes

초록

Matrix codes over a finite field F-q are linear codes defined as subspaces of the vector space of m x n matrices over F-q. In this paper, we show how to obtain self-dual matrix codes from a self-dual matrix code of smaller size using a method we call the building-up construction. We show that every self-dual matrix code can be constructed using this building-up construction. Using this, we classify, that is, we find a complete set of representatives for the equivalence classes of self-dual matrix codes of small sizes. In particular we have classifications for self-dual matrix codes of sizes 2 x 4, 2 x 5 over F-2, of size 2 x 3, 2 x 4 over F-4, of size 2 x 2, 2 x 3 over F-8, and of size 2 x 2, 2 x 3 over F-13, all of which have been left open from K. Morrison's classification.

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