The $q$-ary antiprimitive BCH codes
Hongwei Zhu, Minjia Shi, Xiaoqiang Wang, Tor Helleseth
TL;DR
This paper studies $q$-ary antiprimitive BCH codes over finite fields, analyzing their parameters, providing lower bounds on minimum distance, and solving some open problems related to their optimality.
Contribution
It offers new bounds and partial solutions to open problems on the minimum distance of antiprimitive BCH codes, enhancing understanding of their parameters.
Findings
Provided lower bounds on minimum distance
Identified many optimal linear codes within this class
Partially solved two open problems about minimum distance
Abstract
It is well-known that cyclic codes have efficient encoding and decoding algorithms. In recent years, antiprimitive BCH codes have attracted a lot of attention. The objective of this paper is to study BCH codes of this type over finite fields and analyse their parameters. Some lower bounds on the minimum distance of antiprimitive BCH codes are given. The BCH codes presented in this paper have good parameters in general, containing many optimal linear codes. In particular, two open problems about the minimum distance of BCH codes of this type are partially solved in this paper.
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 · Islamic Finance and Communication · Cryptographic Implementations and Security