Decoding Five Times Extended Reed Solomon Codes Using Syndromes

keywords: Algorithm, extended Reed Solomon codes, error correction decoding, syndromes
Recently a new family of five times extended Reed Solomon codes constructed over certain finite fields GF(2 zeta), where zeta >= 3 is an odd integer, was discovered. Until now only an erasure decoding algorithm for these codes was published. In this paper a new decoding algorithm is presented, which allows correcting up to two errors in a codeword from the five times extended Reed Solomon codes. The proposed decoding algorithm is based on syndrome usage.
mathematics subject classification 2000: 58F15, 58F17, 53C35
reference: Vol. 39, 2020, No. 6, pp. 1311–1335