Creating and implementing efficient decoding algorithms is an important study in Coding Theory. This thesis focuses on the decoding algorithms for Reed-Solomon Codes and Hermitian Codes, specifically the Berlekamp-Massey Algorithm and the Berlekamp-Massey- Sakata Algorithm. The Berlekamp-Massey-Sakata Algorithm alone is not enough to decode up to the minimum distance bound so Feng and Rao's technique of Majority Voting is included to allow decoding up to the minimum distance bound and even beyond for some high rate codes. An implementation for each of these decoding algorithms using the programming language Sage was created with the goal that these could be made available to the community of Sage users.
