Some New Constructions of Quantum MDS Codes
Weijun Fang, Fang-Wei Fu

TL;DR
This paper introduces six new classes of q-ary quantum MDS codes using GRS codes and Hermitian construction, achieving larger minimum distances and longer lengths than previous codes, thus advancing quantum error correction capabilities.
Contribution
Six new classes of quantum MDS codes are constructed with improved parameters, extending the range and performance of quantum error correction codes.
Findings
Minimum distances larger than q/2+1
Longer code lengths than previous constructions
Improved minimum distances for some known codes
Abstract
It is an important task to construct quantum maximum-distance-separable (MDS) codes with good parameters. In the present paper, we provide six new classes of q-ary quantum MDS codes by using generalized Reed-Solomon (GRS) codes and Hermitian construction. The minimum distances of our quantum MDS codes can be larger than q/2+1 Three of these six classes of quantum MDS codes have longer lengths than the ones constructed in [1] and [2], hence some of their results can be easily derived from ours via the propagation rule. Moreover, some known quantum MDS codes of specific lengths can be seen as special cases of ours and the minimum distances of some known quantum MDS codes are also improved as well.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Coding theory and cryptography · Quantum-Dot Cellular Automata
