Construction and Decoding of BCH-Codes Over the Gaussian Field

In this article, first we deliberate the theory of the Gaussian field and extension field of the Gaussian field. Secondly, we provide a comprehensive construction scheme for BCH codes over the Gaussian field. The decoding of newly designed BCH codes is handled through a slightly amended modified Berlekamp-Massey algorithm. The coding gain is obtained by BCH codes over the Gaussian field. Accordingly, a better code rate and the number of code words are obtained as compared to the BCH codes over finite fields. Thus, this makes them a promising candidate for use in communication systems.