Rank error correction up to the Hartmann-Tzeng bound

SEMINARIO DE JÓVENES INVESTIGADORES

Conferenciante: Jose Manuel Muñoz Fuentes (UGR)

Abstract: The theory on error-correcting block codes focuses on how to identify and, if possible, fix errors that might be inserted into fixed-length messages while being sent or stored. Rank codes, which have notable applications on network coding, are known to provide a convenient way to do so. Our approach generalizes the classical family of maximum-rank-distance Gabidulin codes into a larger one, which is endowed with a Hartmann-Tzeng-like lower bound on their rank (and Hamming) distance. For these codes, we develop a syndrome-based error correction algorithm up to the known Hartmann-Tzeng-like bound by decomposing the error-correcting problem into solvable solvable linear algebra ones, including the skew-feedback shift-register synthesis problem. This approach also generalizes previous work on error correction algorithms over skew Reed-Solomon codes (that is, skew-cyclic codes with a Reed-Solomon-like defining set), as those are a subset of the ones studied through our approach.