Lower bound on minimum Lee distance of algebraic–geometric codes over finite fields

Abstract

Algebraic-geometric (AG) codes over finite fields with respect to the Lee metric have been studied. A lower bound on the minimum Lee distance is derived, which is a Lee-metric version of the well-known Goppa bound on the minimum Hamming distance of AG codes. The bound generalises a lower bound on the minimum Lee distance of Lee-metric BCH and Reed-Solomon codes, which have been successfully used for protecting against bitshift and synchronisation errors in constrained channels and for error control in partial-response channels.