# Linear block and convolutional MDS codes to required rate, distance and type

@article{Hurley2021LinearBA, title={Linear block and convolutional MDS codes to required rate, distance and type}, author={Ted Hurley}, journal={ArXiv}, year={2021}, volume={abs/2109.06721} }

Algebraic methods for the design of series of maximum distance separable (MDS) linear block and convolutional codes to required specifications and types are presented. Algorithms are given to design codes to required rate and required error-correcting capability and required types. Infinite series of block codes with rate approaching a given rationalR with 0 < R < 1 and relative distance over length approaching (1−R) are designed. These can be designed over fields of given characteristic p or… Expand

#### References

SHOWING 1-10 OF 60 REFERENCES

Convolutional codes from unit schemes

- Mathematics, Computer Science
- ArXiv
- 2014

Convolutional codes are constructed, designed and analysed using row and/or block structures of unit algebraic schemes and of codes with specific properties are derived, shown algebraically and algebraic decoding methods are derived. Expand

Maximum distance separable codes to order

- Computer Science, Mathematics
- ArXiv
- 2019

Maximum distance separable (MDS) codes of the form $(q-1,r)$ are constructed for any field, encompassing, easy to construct with efficient encoding and decoding algorithms of complexity $t$, where t is the error-correcting capability of the code. Expand

Maximum Distance Separable Convolutional Codes

- Mathematics, Computer Science
- Applicable Algebra in Engineering, Communication and Computing
- 1999

The main result of the paper shows that this upper bound for the free distance generalizing the Singleton bound can be achieved in all cases if one allows sufficiently many field elements. Expand

Construction of Unit-Memory MDS Convolutional Codes

- Computer Science, Mathematics
- ArXiv
- 2015

A large family of unit-memory MDS convolutional codes over $\F$ with flexible parameters is constructed, the field size required to define these codes is much smaller than previous works, and this construction leads to many new strongly-MDS convolutionsal codes. Expand

Constructions of MDS-convolutional codes

- Mathematics, Computer Science
- IEEE Trans. Inf. Theory
- 2001

This correspondence provides an elementary construction of MDS convolutional codes for each rate k/n and each degree /spl delta/. Expand

Complementary Dual Algebraic Geometry Codes

- Computer Science, Mathematics
- IEEE Transactions on Information Theory
- 2018

All the constructed LCD codes from elliptic curves are MDS or almost MDS, which means maximum distance separable (MDS) codes are of the most importance in coding theory due to their theoretical significance and practical interests. Expand

Constructing strongly-MDS convolutional codes with maximum distance profile

- Mathematics, Computer Science
- Adv. Math. Commun.
- 2016

By construction, this paper shows by construction the existence of convolutional codes that are both strongly-MDS and MDP for all choices of parameters. Expand

Linear complementary dual, maximum distance separable codes

- Computer Science, Mathematics
- ArXiv
- 2019

Series of asymptotically good LCD MDS codes are explicitly constructed to required rate and required error-correcting capability. Expand

Euclidean and Hermitian LCD MDS codes

- Mathematics, Computer Science
- Des. Codes Cryptogr.
- 2018

This paper studies the problem of the existence of q-ary [n, k] LCD MDS codes and solves it for the Euclidean case, and investigates several constructions of new Euclidan and Hermitian LCD M DS codes. Expand

Linear Codes Over 𝔽q Are Equivalent to LCD Codes for q>3

- Computer Science, Mathematics
- IEEE Trans. Inf. Theory
- 2018

A general construction of LCD codes from any linear codes is introduced and it is shown that any linear code over $\mathbb F_{q} (q>3)$ is equivalent to a Euclidean LCD code and anylinear code over $q^{2}(q>2)$ (q-ary linear codes) is equivalents to a Hermitian LCD code. Expand