Double and bordered α-circulant self-dual codes over finite commutative chain rings

MICHAEL KIERMAIER, ALFRED WASSERMANN michael.kiermaier, [email protected] Mathematical Department, University of Bayreuth, D-95440 Bayreuth, GERMANY Abstract. In this paper we investigate codes over finite commutative rings R, whose generator matrices are built from α-circulant matrices. For a non-trivial ideal I < R we give a method to lift such codes over R/I to codes over R, such that some isomorphic copies are avoided. For the case where I is the minimal ideal of a finite chain ring we refine this lifting method: We impose the additional restriction that lifting preserves self-duality. It will be shown that this can be achieved by solving a linear system of equations over a finite field. Finally we apply this technique to Z4-linear double nega-circulant and bordered circulant self-dual codes. We determine the best minimum Lee distance of these codes up to length 64.