TL;DR
This paper introduces new linear codes over Hurwitz integers with a novel Hurwitz metric, suitable for QAM-type modulation schemes, and develops decoding algorithms for errors affecting up to two coordinates.
Contribution
It presents new classes of codes over Hurwitz integers with a specialized metric and decoding algorithms for error correction in QAM-based communication systems.
Findings
New classes of codes over Hurwitz integers are constructed.
A decoding algorithm for up to two errors in Hurwitz metric is proposed.
The codes are applicable to QAM-type modulation schemes.
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 Hurwitz metric. The codes with respect to Hurwitz metric use in coded modu- lation schemes based on quadrature amplitude modulation (QAM)-type constellations, for which neither Hamming metric nor Lee metric. Also, we define decoding algorithms for these codes when up to two coordinates of a transmitted code vector are effected by error of arbitrary Hurwitz weight.
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