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.
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Taxonomy
TopicsCoding theory and cryptography · Finite Group Theory Research · graph theory and CDMA systems
