# On deep holes of projective Reed-Solomon codes

@article{Zhang2016OnDH, title={On deep holes of projective Reed-Solomon codes}, author={Jiandi Zhang and Daqing Wan}, journal={2016 IEEE International Symposium on Information Theory (ISIT)}, year={2016}, pages={925-929} }

In this paper, we obtain new results on the covering radius and deep holes for projective Reed-Solomon (PRS) codes.

## Topics from this paper

## 7 Citations

On deep-holes of Gabidulin codes

- Mathematics, Computer ScienceFinite Fields Their Appl.
- 2018

In this paper, we determine the covering radius and a class of deep holes for Gabidulin codes with both rank metric and Hamming metric. Moreover, we give a necessary and sufficient condition for…

Explicit Deep Holes of Reed-Solomon Codes

- Mathematics, Computer ScienceArXiv
- 2017

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.…

Deep Holes of Projective Reed-Solomon Codes

- Computer ScienceIEEE Transactions on Information Theory
- 2020

This paper uses algebraic methods to explicitly construct three classes of deep holes for PRS codes with redundancy four, and shows that these three classes completely classify all deep holes of PRS code with redundancyFour.

On deep holes of generalized projective Reed-Solomon codes

- Computer Science, MathematicsArXiv
- 2017

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 $\#(I)=k$.

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

- Mathematics, Computer ScienceArXiv
- 2020

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

- Computer Science, MathematicsIEEE Transactions on Information Theory
- 2021

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.

On the weight distribution of the cosets of MDS codes

- Computer Science, MathematicsAdvances in Mathematics of Communications
- 2021

The Bonneau formula is transformed into a more structured and convenient form and it is proved that all the cosets of weight of the MDS code have the same weight distribution.

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