Self-dual codes from a block matrix construction characterised by group rings

Abstract

We give a new technique for constructing self-dual codes based on a block matrix whose blocks arise from group rings and orthogonal matrices. The technique can be used to construct self-dual codes over finite commutative Frobenius rings of characteristic 2. We give and prove the necessary conditions needed for the technique to produce self-dual codes. We also establish the connection between self-dual codes generated by the new technique and units in group rings. Using the construction together with the building-up construction, we obtain new extremal binary self-dual codes of lengths 64, 66 and 68 and new best known binary self-dual codes of length 80.