Double and bordered alpha-circulant self-dual codes over finite commutative chain rings
- In this paper we investigate codes over finite commutative rings R, whose generator matrices are built from alpha-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.
Construction of Two-Weight Codes
- This is a talk given at the conference: Algebra and Computation 2005 in Tokyo. We describe a method for the construction of two-weight 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.