New Quasi-Cyclic Codes from Simplex Codes
Eric Zhi Chen
TL;DR
This paper introduces new multi-generator quasi-cyclic codes derived from simplex codes, resulting in codes with improved minimum distance bounds for binary linear codes.
Contribution
It extends the study of quasi-cyclic codes to 2- and 3-generator cases and constructs new codes with better bounds from simplex codes.
Findings
Constructed 5-generator QC [93, 17, 34] and [254, 23, 102] codes.
Developed related codes [96, 17, 36] and [256, 23, 104].
Improved bounds on maximum minimum distance for binary linear codes.
Abstract
As a generalization of cyclic codes, quasi-cyclic (QC) codes contain many good linear codes. But quasi-cyclic codes studied so far are mainly limited to one generator (1-generator) QC codes. In this correspondence, 2-generator and 3-generator QC codes are studied, and many good, new QC codes are constructed from simplex codes. Some new binary QC codes or related codes, that improve the bounds on maximum minimum distance for binary linear codes are constructed. They are 5-generator QC [93, 17, 34] and [254, 23, 102] codes, and related [96, 17, 36], [256, 23, 104] 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 · graph theory and CDMA systems · Cryptographic Implementations and Security