Eisenstein field BCH codes construction and decoding
Muhammad Sajjad, Tariq Shah, Qin Xin, Bander Almutairi
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>
Topics & Concepts
BCH codeDecoding methodsComputer scienceReed–Solomon error correctionField (mathematics)Berlekamp–Welch algorithmExtension (predicate logic)ArithmeticError detection and correctionAlgorithmDiscrete mathematicsMathematicsLinear codeBlock codeProgramming languagePure mathematicsError Correcting Code TechniquesCoding theory and cryptographyAdvanced Wireless Communication Techniques