The support designs of the triply even codes of length 48
Tsuyoshi Miezaki, Hiroyuki Nakasora
TL;DR
This paper explores the support designs of triply even binary codes of length 48, providing examples where all weight classes support 1-designs and some duals support 2-designs, advancing understanding of combinatorial structures in these codes.
Contribution
It presents specific examples of triply even codes of length 48 with support designs, including duals with 2-design support, based on classification by Betsumiya and Munemasa.
Findings
All weight classes support 1-designs.
Dual codes include classes supporting 2-designs.
Examples are based on classified codes of length 48.
Abstract
In this paper, we present examples of codes all of whose weight classes support 1-designs, with duals whose classes include two that support 2-designs. We can find these examples in the triply even binary codes of length 48, which have been classified by Betsumiya and Munemasa.
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 · Finite Group Theory Research · graph theory and CDMA systems