# Subfield-subcodes of Generalized Toric codes

@article{Hernando2010SubfieldsubcodesOG, title={Subfield-subcodes of Generalized Toric codes}, author={Fernando Hernando and Michael E. O'Sullivan and Emanuel M. Popovici and Shraddha Srivastava}, journal={2010 IEEE International Symposium on Information Theory}, year={2010}, pages={1125-1129} }

We study subfield-subcodes of Generalized Toric (GT) codes over Fps . These are the multidimensional analogues of BCH codes, which may be seen as subfield-subcodes of generalized Reed-Solomon codes [2], [3], [6], [10], [11]. We identify polynomial generators for subfield-subcodes of GT codes which allows us to determine the dimensions and obtain bounds for the minimum distance. We give several examples of binary and ternary subfield-subcodes of GT codes that are the best known codes of a given…

## 11 Citations

On the subfield subcodes of Hermitian codes

- Computer ScienceDes. Codes Cryptogr.
- 2014

Some of the subfield subcodes of Hermitian codes are at least as good as the previously known codes, and the existence of good long codes is shown.

The dimension of subcode-subfields of shortened generalized Reed–Solomon codes

- Computer ScienceDes. Codes Cryptogr.
- 2013

It is shown that a particular class of GRS codes produces many SFSC with large dimension, and two algorithms for searching through these codes are presented and a list of new best-known codes obtained.

Quantum codes from affine variety codes and their subfield-subcodes

- Computer ScienceDes. Codes Cryptogr.
- 2015

Fine variety codes and their subfield-subcodes are used to obtain quantum stabilizer codes via the CSS code construction with good parameters, some of them exceeding the CSS quantum Gilbert–Varshamov bound.

Simplified decoding techniques for linear block codes

- Computer Science
- 2013

This thesis focuses on reducing the computational effort and enhancing the efficiency of decoding algorithms for several codes from algorithmic as well as architectural standpoint and explores a method of constructing optimal codes by computing the subfield subcodes of Generalized Toric codes that is a natural extension of RS codes over several dimensions.

Fulcrum Network Codes: A Code for Fluid Allocation of Complexity

- Computer ScienceArXiv
- 2014

Fulcrum network codes have a unique trait missing so far in the network coding literature: they provide the network with the flexibility to spread computational complexity over different devices depending on their current load, network conditions, or even energy targets in a decentralized way.

Aalborg Universitet Fulcrum Flexible Network Coding for Heterogeneous Devices

- Computer Science
- 2018

Fulcrum has a unique trait missing so far in the network coding literature: providing the network with the flexibility to distribute computational complexity over different devices depending on their current load, network conditions, or energy constraints.

Classical and Quantum Error-Correction Coding in Genetics

- Computer Science
- 2016

This chapter starts with the description of using the concepts from both classical and quantum information theories to describe the evolution of biological channel capacity through generations, and describes the use of nonbinary quantum stabilizer codes to deal with nucleobase substitution errors.

Fulcrum: Flexible Network Coding for Heterogeneous Devices

- Computer ScienceIEEE Access
- 2018

Fulcrum has a unique trait missing so far in the network coding literature: providing the network with the flexibility to distribute computational complexity over different devices depending on their current load, network conditions, or energy constraints.

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