# 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.

## 23 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.

### 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.

### Duality of generalized twisted Reed-Solomon codes and Hermitian self-dual MDS or NMDS codes

- Computer ScienceCryptography and Communications
- 2022

This paper investigates the duality properties of generalized twisted Reed-Solomon (abbreviated GTRS) codes in some special cases and a new systematic approach is proposed to draw Hermitian self-dual (+)-GTRS codes.

## References

SHOWING 1-10 OF 28 REFERENCES

### 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…

### A construction of non-Reed-Solomon type MDS codes

- Computer ScienceIEEE Trans. Inf. Theory
- 1989

A construction is presented of long maximum-distance-separable (MDS) codes that are not generalized Reed-Solomon (GRS) type that use subsets of a finite field F=GF(q) with the property that no t distinct elements of S add up to some fixed element of F.

### On MDS codes via Cauchy matrices

- Computer Science, MathematicsIEEE Trans. Inf. Theory
- 1989

A special form of Cauchy matrix is used to obtain a tighter bound for the validity region of the maximum distance separable (MDS) conjecture and a new compact characterization of generalized…

### Twisted BCH‐codes

- Computer Science
- 1997

The theory of a generalization of the notion of BCHcode to additive codes, which are not necessarily linear, is developed and demonstrated by constructing a large number of record-breaking linear codes via concatenation.

### On the complexity of decoding Reed-Solomon codes (Corresp.)

- Computer ScienceIEEE Trans. Inf. Theory
- 1976

Certain q -ary Reed-Solomon codes can be decoded by an algorithm requiring only O(q \log^{2} q) additions and multiplications in GF(q) .

### A new family of linear maximum rank distance codes

- Computer ScienceAdv. Math. Commun.
- 2016

A new family of linear maximum rank distance (MRD) codes for all parameters is constructed, which contains the only known family for general parameters, the Gabidulin codes, and contains codes inequivalent to the Gabdulin codes.

### Maximum distance q -nary codes

- Computer ScienceIEEE Trans. Inf. Theory
- 1964

Examples and construction methods are given to show that these codes exist for a number of values of q, k, and r and with the restriction that the codes be linear.

### On generator matrices of MDS codes

- Computer Science, MathematicsIEEE Trans. Inf. Theory
- 1985

By taking rectangular subarrays of the described triangles, it is possible to construct generator matrices [I|A] of maximum distance separable codes, where A is a Hankel matrix.

### Squares of Random Linear Codes

- Computer Science, MathematicsIEEE Transactions on Information Theory
- 2015

A positive answer is given, for codes of dimension k and length roughly (1/2)k2 or smaller, that the square of a code typically fill the whole space.

### Distinguisher-based attacks on public-key cryptosystems using Reed–Solomon codes

- Computer Science, MathematicsDes. Codes Cryptogr.
- 2014

An alternative to Sidelnikov and Shestakov attack is given by building a filtration which enables to completely recover the support and the non-zero scalars defining the secret generalized Reed–Solomon code.