New MDS Euclidean and Hermitian self-dual codes over finite fields
Hongxi Tong, Xiaoqing Wang
TL;DR
This paper introduces new maximum distance separable (MDS) Euclidean and Hermitian self-dual codes over finite fields, expanding the known classes through constructions from cyclic, Reed-Solomon, and constacyclic codes.
Contribution
It presents novel constructions of MDS Euclidean and Hermitian self-dual codes using extended cyclic duadic, Reed-Solomon, and constacyclic codes, enhancing existing code families.
Findings
Many new MDS Euclidean self-dual codes constructed
New MDS Hermitian self-dual codes derived from generalized Reed-Solomon codes
Results on extended cyclic duadic codes' Hermitian self-duality
Abstract
In this paper, we construct MDS Euclidean self-dual codes which are extended cyclic duadic codes. And we obtain many new MDS Euclidean self-dual codes. We also construct MDS Hermitian self-dual codes from generalized Reed-Solomon codes and constacyclic codes. And we give some results on Hermitian self-dual codes, which are the extended cyclic duadic codes.
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
TopicsCoding theory and cryptography · Cooperative Communication and Network Coding · Finite Group Theory Research