Double and bordered alpha-circulant self-dual codes over finite commutative chain rings
Michael Kiermaier, Alfred Wassermann · arXiv (Cornell University) · 2008
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 Z 4 -linear double nega-circulant and bordered circulant self-dual codes.We determine the best minimum Lee distance of these codes up to length 64.