On the existence of MDS codes over small fields with constrained generator matrices

@article{Dau2014OnTE,
  title={On the existence of MDS codes over small fields with constrained generator matrices},
  author={Son Hoang Dau and Wentu Song and Chau Yuen},
  journal={2014 IEEE International Symposium on Information Theory},
  year={2014},
  pages={1787-1791}
}
We study the existence over small fields of Maximum Distance Separable (MDS) codes with generator matrices having specified supports (i.e. having specified locations of zero entries). This problem unifies and simplifies the problems posed in recent works of Yan and Sprintson (NetCod'13) on weakly secure cooperative data exchange, of Halbawi et al. (arxiv'13) on distributed Reed-Solomon codes for simple multiple access networks, and of Dau et al. (ISIT'13) on MDS codes with balanced and sparse… CONTINUE READING
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