Elise Reuterskiöld: Reed-Solomon Codes

Abstract.

Reed-Solomon codes are a class of error-correcting codes widely used in digital communication and storage systems due to their ability to detect and correct multiple errors that occur during transmission. This paper provides a comprehensive overview of the theoretical foundation, encoding and decoding processes of cyclic Reed-Solomon codes over Galois fields. Two decoding methods are analyzed, the Direct method and the Euclidean method. Their theoretical structure are discussed in detail, including syndrome computation, error locator and error magnitude polynomials and error correction limits. To evaluate practical performance, both methods were implemented in Python and their computational efficiency was compared under varying parameters such as Galois field order, block length and number of errors. The results show that the Euclidean method scales more efficiently with increasing possible and actual errors, making it more suitable for real-world applications involving high error rates. Finally, implementation challenges are explored along with an analysis of how algorithmic choices affect performance and reliability.