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Construction of TwoWeight Codes
(2005)

Axel Kohnert
 This is a talk given at the conference: Algebra and Computation 2005 in Tokyo. We describe a method for the construction of twoweight codes. This also allows to realize certain strongly regular graphs or equivalently certain point sets in the a finite projective geometry. We use the method of prescibed automorphisms, which allows us to reduce the problem to a size where we can use powerful Diophantine equation solvers provided by Alfred Wassermann.

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.