On deep holes of projective Reed-Solomon codes

@article{Zhang2016OnDH,
  title={On deep holes of projective Reed-Solomon codes},
  author={Jun Zhang and Daqing Wan},
  journal={2016 IEEE International Symposium on Information Theory (ISIT)},
  year={2016},
  pages={925-929}
}
  • Jun ZhangD. Wan
  • Published 9 May 2016
  • Computer Science
  • 2016 IEEE International Symposium on Information Theory (ISIT)
In this paper, we obtain new results on the covering radius and deep holes for projective Reed-Solomon (PRS) codes. 

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A method to construct deep holes for elliptic curve codes and it is conjecture that this construction is complete in the sense that it gives all deep holes.

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D\"ur's theorem on the relation between the covering radius and minimum distance of the GPRS_q(D, k) is shown to be nonzero for any subset $I\subseteq D$ with $\#(I)=k$.

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On integral weight spectra of the MDS codes cosets of weight 1, 2, and 3

The weight of a coset of a code is the smallest Hamming weight of any vector in the coset, and integral weight spectrum the overall numbers of weight w vectors in all the cosets of a fixed weight is called.

On Cosets Weight Distribution of Doubly-Extended Reed-Solomon Codes of Codimension 4

It is proved that the difference between the w-th components of the distributions is uniquely determined by the Difference between the 3-rd components, which implies an interesting (and in some sense unexpected) symmetry of the obtained distributions.

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