Explicit Deep Holes of Reed-Solomon Codes

Jun Zhang; Daqing Wan

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arXiv · 1711.02292

Explicit Deep Holes of Reed-Solomon Codes

Jun Zhang·Daqing Wan

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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 $1$) of the deep holes of PRS codes with redundancy four are also obtained.

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Jun Zhang, Daqing Wan. 2017-11-07. Explicit Deep Holes of Reed-Solomon Codes. https://arxiv.org/abs/1711.02292

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