Self-dual RkRk lifts of binary self-dual codes

In this paper, we give a method to lift binary self-dual codes to the ring RkRk. The lifting method requires solving a system of linear equations over RkRk. This technique is applied to [14,7,4][14,7,4] binary self-dual code to obtain self-dual codes over R2R2. As Gray images of these codes, a substantial number of [56,28,10][56,28,10] self-dual codes are generated. By using the extension theorem given by Bouyuklieva and Bouyukliev in [2], ten new extremal binary self-dual codes of length 58 with new enumerators are found which were not previously known to exist.