Fractional decoding and the Rosenbloom-Tsfasman metric

Abstract

In this paper, we consider the problem of recovering data from partial information considering array codes in the metric space M l,n (Fq) endowed with the Rosenbloom-Tsfasman metric (RT-metric), which are called RT array codes. To be more precise, we want to recover the original data from a received word under the constraint that the decoder can download only an α proportion of the received word. This is called fractional decoding.We show that for any (n, k, l) maximum RT distance separable array code, it is possible to utilize just an α-proportion of the received corrupted codeword to decoding without losing the RT-error correcting capability. Furthermore, we introduce a novel probabilistic fractional decoding algorithm designed to handle random errors. This new algorithm exhibits the ability to correct a larger number of errors compared to the α-decoding radius of (n, k, l) MDS Hamming metric array codes.