Eisenstein field BCH codes construction and decoding

Muhammad Sajjad, Tariq Shah, Qin Xin, Bander Almutairi

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)29453-29473
Number of pages21
JournalAIMS Mathematics
Issue number12
Publication statusPublished - 2023


  • Eisenstein integers
  • Eisenstein field
  • BCH codes over Eisenstein field
  • Berlekamp-Massey algorithm


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