Two classes of reducible cyclic codes with large minimum symbol-pair distances
Abstract
The high-density data storage technology aims to design high-capacity storage at a relatively low cost. In order to achieve this goal, symbol-pair codes were proposed by Cassuto and Blaum \cite{CB10,CB11} to handle channels that output pairs of overlapping symbols. Such a channel is called symbol-pair read channel, which introduce new concept called symbol-pair weight and minimum symbol-pair distance. In this paper, we consider the parameters of two classes of reducible cyclic codes under the symbol-pair metric. Based on the theory of cyclotomic numbers and Gaussian period over finite fields, we show the possible symbol-pair weights of these codes. Their minimum symbol-pair distances are twice the minimum Hamming distances under some conditions. Moreover, we obtain some three symbol-pair weight codes and determine their symbol-pair weight distribution. A class of MDS symbol-pair codes is also established. Among other results, we determine the values of some generalized cyclotomic numbers.
Cite
@article{arxiv.2309.04068,
title = {Two classes of reducible cyclic codes with large minimum symbol-pair distances},
author = {Xiaoqiang Wang and Yue Su and Dabin Zheng and Wei Lu},
journal= {arXiv preprint arXiv:2309.04068},
year = {2023}
}