Decoding of Interleaved Alternant Codes [article]

Lukas Holzbaur, Hedongliang Liu, Alessandro Neri, Sven Puchinger, Johan Rosenkilde, Vladimir Sidorenko, Antonia Wachter-Zeh
2021 arXiv   pre-print
Interleaved Reed-Solomon codes admit efficient decoding algorithms which correct burst errors far beyond half the minimum distance in the random errors regime, e.g., by computing a common solution to the Key Equation for each Reed-Solomon code, as described by Schmidt et al. If this decoder does not succeed, it may either fail to return a codeword or miscorrect to an incorrect codeword, and good upper bounds on the fraction of error matrices for which these events occur are known. The decoding
more » ... lgorithm immediately applies to interleaved alternant codes as well, i.e., the subfield subcodes of interleaved Reed-Solomon codes, but the fraction of decodable error matrices differs, since the error is now restricted to a subfield. In this paper, we present new general lower and upper bounds on the fraction of error matrices decodable by Schmidt et al.'s decoding algorithm, thereby making it the only decoding algorithm for interleaved alternant codes for which such bounds are known.
arXiv:2010.07142v2 fatcat:5kmj2swu4vgd3lwuaqytjshf6u