Codes in Rosenbloom-Tsfasman metric: A Survey

Abstract

This paper gives a systematic survey of research carried out in the theory of codes equipped with Rosenbloom-Tsfasman metric. In classical coding theory setting, codes are investigated with respect to the Hamming metric which can efficiently address the communication problems arising from channels in which channel noise generates equiprobable errors. But however, not all the real world channels are of that nature, especially, when the possible errors form patterns of a specific shape. Rosenbloom and Tsfasman introduced a non-Hamming metric, called Rosenbloom-Tsfasman metric (RT-metric, in short) that can address the problem of reliable information transmission over parallel noisy channels. Martin, Stinson and Skriganov independently introduced the same metric in the context of the theory of uniform distributions. As this metric happened to be a generalization of the classical Hamming metric, it has attracted so much attention from the coding theory research community and as a result a lot of work has been done in this line of research over the past 3 decades. In this paper we would like to present the key developments in the field of codes with RT-metric.