# 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} }

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

## 12 Citations

### Explicit Deep Holes of Reed-Solomon Codes

- 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.…

### On Deep Holes of Elliptic Curve Codes

- Computer Science, MathematicsArXiv
- 2022

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.

### Finite Geometry and Deep Holes of Reed-Solomon Codes over Finite Local Rings

- Mathematics, Computer ScienceCommunications in Mathematical Research
- 2022

This paper proposes the maximum arc problem, normal rational curve conjecture, and extensions of normal rational curves over finite local rings, analogously to the finite geometry over finite fields, and studies the deep hole problem of generalized Reed-Solomon codes over finiteLocal rings.

### On deep holes of primitive projective Reed-Solomon codes

- Computer ScienceSCIENTIA SINICA Mathematica
- 2018

A class of deepholes of primitive projective Reed-Solomon codes is obtained by using the generating matrix of maximaldistance separable codes over the finite field $\mathbb{F}_q$ and Vandermonde determinant.

### On deep holes of generalized projective Reed-Solomon codes

- 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 $\#(I)=k$.

### MDS, Near-MDS or 2-MDS Self-Dual Codes via Twisted Generalized Reed-Solomon Codes

- Computer ScienceIEEE Transactions on Information Theory
- 2022

A sufficient and necessary condition that a twisted Reed-Solomon (TRS) code with two twists is MDS is characterized and some constructions of self-dual TGRS codes are presented, which are MDS, NMDS or 2-MDS.

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

- 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 ScienceIEEE 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 ScienceAdvances 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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