11T71 Algebraic coding theory; cryptography
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Double and bordered alphacirculant selfdual codes over finite commutative chain rings
(2008)

Michael Kiermaier
Alfred Wassermann
 In this paper we investigate codes over finite commutative rings R, whose generator matrices are built from alphacirculant matrices. For a nontrivial 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 selfduality. 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_4linear double negacirculant and bordered circulant selfdual codes. We determine the best minimum Lee distance of these codes up to length 64.