BCH Codes for the Rosenbloom–Tsfasman Metric
Wei Zhou, Shu Lin, Khaled Abdel-Ghaffar · IEEE Transactions on Information Theory · 2016
The Rosenbloom-Tsfasman metric has attracted the attention of many researchers as a generalization of the Hamming metric that is relevant to practical problems. Codes for this metric were considered. In particular, Reed-Solomon codes were generalized to be compatible with this metric. In this paper, a generalization of BCH codes for the Rosenbloom-Tsfasman metric is proposed. This generalization is based on considering BCH codes as subfield subcodes of Reed-Solomon codes. By characterizing these subfield subcodes, an explicit construction of BCH codes for the Rosenbloom-Tsfasman metric is provided. Two important properties of Reed-Solomon codes and BCH codes for the Rosenbloom-Tsfasman metric are studied and compared with those for the Hamming metric. These properties are cyclic structure and duality. The approach is based on Galois-Fourier transforms associated with Hasse derivatives.