Maximum Distance Separable Codes for $b$-Symbol Read Channels
Information Theory
2016-09-30 v1 math.IT
Abstract
Recently, Yaakobi et al. introduced codes for -symbol read channels, where the read operation is performed as a consecutive sequence of symbols. In this paper, we establish a Singleton-type bound on -symbol codes. Codes meeting the Singleton-type bound are called maximum distance separable (MDS) codes, and they are optimal in the sense they attain the maximal minimum -distance. Based on projective geometry and constacyclic codes, we construct new families of linear MDS -symbol codes over finite fields. And in some sense, we completely determine the existence of linear MDS -symbol codes over finite fields for certain parameters.
Cite
@article{arxiv.1609.09236,
title = {Maximum Distance Separable Codes for $b$-Symbol Read Channels},
author = {Baokun Ding and Tao Zhang and Gennian Ge},
journal= {arXiv preprint arXiv:1609.09236},
year = {2016}
}