MDS or NMDS self-dual codes from twisted generalized Reed–Solomon codes

New MDS Self-Dual Codes from Generalized Reed-Solomon Codes

Both MDS and Euclidean self-dual codes have theoretical and practical importance and the study of MDS self-dual codes has attracted lots of attention in recent years. In particular, determining existence of q-ary MDS self-dual codes for various lengths has been investigated extensively. The problem is completely solved for the case where q is even. The current paper focuses on the case where q ...

Orthogonal designs and MDS self-dual codes

MDS and self-dual codes over rings

In this paper we give the structure of constacyclic codes over formal power series and chain rings. We also present necessary and sufficient conditions on the existence of MDS codes over principal ideal rings. These results allow for the construction of infinite families of MDS self-dual codes over finite chain rings, formal power series and principal ideal rings.

Construction of MDS self-dual codes from orthogonal matrices

In this paper, we give algorithms and methods of construction of self-dual codes over finite fields using orthogonal matrices. Randomization in the orthogonal group, and code extension are the main tools. Some optimal, almost MDS, and MDS self-dual codes over both small and large prime fields are constructed.

Generalized Twisted Gabidulin Codes

Based on the twisted Gabidulin codes obtained recently by Sheekey, we construct a new family of maximal rank distance codes as a set of qpolynomials over Fqn , which includes the generalized Gabidulin codes and the twisted Gabidulin codes. Their Delsarte duals and adjoint codes are investigated. We also obtain necessary and sufficient conditions for the equivalence between two members of our ne...