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Explicit Deep Holes of Reed-Solomon Codes

Information Theory 2017-11-08 v1 math.IT

Abstract

In this paper, deep holes of Reed-Solomon (RS) codes are studied. A new class of deep holes for generalized affine RS codes is given if the evaluation set satisfies certain combinatorial structure. Three classes of deep holes for projective Reed-Solomon (PRS) codes are constructed explicitly. In particular, deep holes of PRS codes with redundancy three are completely obtained when the characteristic of the finite field is odd. Most (asymptotically of ratio 11) of the deep holes of PRS codes with redundancy four are also obtained.

Keywords

Cite

@article{arxiv.1711.02292,
  title  = {Explicit Deep Holes of Reed-Solomon Codes},
  author = {Jun Zhang and Daqing Wan},
  journal= {arXiv preprint arXiv:1711.02292},
  year   = {2017}
}

Comments

31 pages

R2 v1 2026-06-22T22:38:15.657Z