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On the Assmus--Mattson type theorem for Type I and even formally self-dual codes (2208.08617v2)
Published 18 Aug 2022 in math.CO, cs.IT, math.GR, and math.IT
Abstract: In the present paper, we give the Assmus--Mattson type theorem for near-extremal Type I and even formally self-dual codes. We show the existence of $1$-designs or $2$-designs for these codes. As a corollary, we prove the uniqueness of a self-orthogonal $2$-$(16,6,8)$ design.