2014/06/05 by Tufekci, Nesibe, Yildiz, Bahattin
#94B05 #94B99 #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.1406.1281
In this work, we study codes over the ring Rk,m=F2[u,v]/, which is a family of Frobenius, characteristic 2 extensions of the binary field. We introduce a distance and duality preserving Gray map from Rk,m to F2km together with a Lee weight. After proving the MacWilliams identities for codes over Rk,m for all the relevant weight enumerators, we construct many binary self-dual codes as the Gray images of self-dual codes over Rk,m. In addition to many extremal binary self-dual codes obtained in this way, including a new construction for the extended binary Golay code, we find 175 new Type I binary self-dual codes of parameters [72,36,12] and 105 new Type II binary self-dual codes of parameter [72,36,12].