Double bordered constructions of self-dual codes from group rings over Frobenius rings

Abstract

AbstractIn this work, we describe a double bordered construction of self-dual codes from group rings. We show that this construction is effective for groups of order 2p where p is odd, over the rings $\mathbb {F}_{2}+u\mathbb {F}_{2}$ F 2 + u F 2 and $\mathbb {F}_{4}+u\mathbb {F}_{4}$ F 4 + u F 4 . We demonstrate the importance of this new construction by finding many new binary self-dual codes of lengths 64, 68 and 80; the new codes and their corresponding weight enumerators are listed in several tables.