Codes over Hurwitz integers

Abstract In this study, we obtain new classes of linear codes over Hurwitz integers equipped with a new metric. We refer to the metric as the Hurwitz metric. Also, we define decoding algorithms for these codes when up to two coordinates of a transmitted code vector are affected by the error of arbitrary Hurwitz weight. The interest in the codes with respect to the Hurwitz metric is their use in coded modulation schemes based on quadrature amplitude modulation (QAM)-type constellations where the Hamming metric and the Lee metric are not appropriate.