Abstract
<abstract> <p>First, we will go through the theory behind the Eisenstein field (EF) and its extension field. In contrast, we provide a detailed framework for building BCH codes over the EF in the second stage. BCH codes over the EF are decoded using the Berlekamp-Massey algorithm (BMA) in this article. We investigate the error-correcting capabilities of these codes and provide expressions for minimal distance. We provide researchers and engineers creating and implementing robust error-correcting codes for digital communication systems with detailed information on building, decoding and performance assessment.</p> </abstract>
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