Double Bordered Constructions of Self-Dual Codes from Group Rings over Frobenius Rings

This is a post-peer-review, pre-copyedit version of an article published in Cryptography and Communications. The final authenticated version is available online at: http://dx.doi.org/10.1007/s12095-019-00420-3In 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 F2 + uF2 and F4 + uF4. 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 table

The (+)(+)-extended twisted generalized Reed-Solomon code

In this paper, we give a parity check matrix for the $(+)$-extended twisted generalized Reed Solomon (in short, ETGRS) code, and then not only prove that it is MDS or NMDS, but also determine the weight distribution. Especially, based on Schur method, we show that the $(+)$-ETGRS code is not GRS or EGRS. Furthermore, we present a sufficient and necessary condition for any punctured code of the $(+)$-ETGRS code to be self-orthogonal, and then construct several classes of self-dual $(+)$-TGRS codes and almost self-dual $(+)$-ETGRS codes

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

From Springer Nature via Jisc Publications RouterHistory: received 2019-06-03, accepted 2019-12-05, registration 2019-12-06, online 2020-01-09, pub-electronic 2020-01-09, pub-print 2020-07Publication status: PublishedAbstract: In 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 F2+uF2 and F4+uF4. 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