Magma implementation of decoding algorithms for general algebraic geometry codes

Abstract

Goppa's codes on algebraic curves defined over finite fields, called AG codes, are usually regarded as the most successful class of error correcting codes in theory as well as in practice. Despite the splendid history of theoretic achievements though, an efficient algorithm decoding general AG codes appeared only recently. The decoding algorithm requires some precomputed data about the Riemann-Roch spaces of functions or differentials of the given curve of positive genus. As Magma is particularly good at computing with these spaces, the algorithm was implemented on Magma. We present its Magma implementation and describe certain details of the implementation. © 2014 Springer-Verlag.