Explicit Constructions of MDS Self-Dual Codes
Lin Sok · IEEE Transactions on Information Theory · 2019
In this paper, we study self-dual codes over finite fields using tools from algebraic function fields in one variable. An algebraic geometry code of length n is defined using two divisors G and D = P1+ ⋯ + Pn. We characterize self-orthogonality of the genus zero code in terms of the divisors G, D and the value of a well-chosen derivative polynomial at points (Pi)1≤i≤n. We explore the existence problem of MDS self-dual codes in the odd characteristic case, and we explicitly construct families of new MDS self-dual codes.