# Twisted reed-solomon codes

@article{Beelen2017TwistedRC, title={Twisted reed-solomon codes}, author={Peter Beelen and Sven Puchinger and Johan Sebastian Rosenkilde}, journal={2017 IEEE International Symposium on Information Theory (ISIT)}, year={2017}, pages={336-340} }

We present a new general construction of MDS codes over a finite field Fq. We describe two explicit subclasses which contain new MDS codes of length at least q/2 for all values of q ≥ 11. Moreover, we show that most of the new codes are not equivalent to a Reed-Solomon code.

## 29 Citations

### Multi-twisted Reed-Solomon codes with small dimensional hull

- Mathematics, Computer ScienceArXiv
- 2022

A necessary and sufficient condition for multi-twisted Reed-Solomon codes to be MDS is found and necessary conditions for the existence of multi-Twisted RS codes with zero and one-dimensional hulls are obtained.

### Generalised Twisted Gabidulin Codes

- Computer ScienceArXiv
- 2017

We present a new family of maximum rank distance (MRD) codes. The new class contains codes that are neither equivalent to a generalised Gabidulin nor to a twisted Gabidulin code, the only two known…

### Further Generalisations of Twisted Gabidulin Codes

- Computer Science
- 2017

We present a new family of maximum rank distance (MRD) codes. The new class contains codes that are neither equivalent to a generalised Gabidulin nor to a twisted Gabidulin code, the only two known…

### Hulls of special typed linear codes and constructions of new EAQECCs

- Computer ScienceArXiv
- 2022

Empirical studies of Euclidean and Hermitian hulls of generalized Reed-Solomon codes and twisted generalized Reed, Roth-Lempel typed codes, and explicit constructions of MDS and AMDS linear codes for which their hull dimensions are well determined are presented.

### Structural Properties of Twisted Reed-Solomon Codes with Applications to Cryptography

- Computer Science2018 IEEE International Symposium on Information Theory (ISIT)
- 2018

It is proved that the code class contains a large subfamily that is closed under duality, and it is single out a subfamily of the new codes which could be considered for code-based cryptography.

### On twisted generalized Reed-Solomon codes with l twists

- Computer Science, MathematicsArXiv
- 2022

This paper studies a class of twisted generalized Reed-Solomon (TGRS) codes with general ℓ twists, and gives an explicit construction of self-dual TGRS codes.

### Self-dual twisted generalized Reed-Solomon codes

- Computer ScienceArXiv
- 2021

By using some properties for linear algebra methods, the parity-check matrices for twisted generalized Reed-Solomon codes with any given hook h and twist t are presented, and a necessary condition for the twisted summarized Reed- Solomon code with h ≥ t to be self-dual is given.

### MDS or NMDS LCD codes from twisted Reed-Solomon codes

- Computer ScienceCryptography and Communications
- 2022

This paper gives check matrices of twisted generalized Reed-Solomon codes and construct three classes of new LCD MDS codes from twisted generalized RoS Solomon codes, including LCD NMDS codes.

### Twisted Hermitian Codes

- Computer ScienceMathematics
- 2020

A family of codes, which are based on Hermitian codes and inspired by the twisted Reed–Solomon codes, are defined, and it is demonstrated that these new codes can have high-dimensional Schur squares and an identified subfamily of twisted Hermitians that achieves a Schur square dimension close to that of a random linear code.

### Self-orthogonal generalized twisted Reed-Solomon codes

- Computer ScienceArXiv
- 2022

This paper gives a sufficient and necessary condition for the generalized twisted Reed-Solomon code with h + t ≤ k − 1 to be self-orthogonal, and shows that there is no self- orthogonal generalized twisting Reed- Solomon code under some conditions.

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