A note on the Assmus--Mattson theorem for some ternary codes (a resume)

TL;DR

This paper investigates the limitations of the Assmus--Mattson theorem when applied to certain ternary codes, establishing an upper bound on the design strength and characterizing the ternary Golay code.

Contribution

It provides a new upper bound on the design strength for two and three-weight ternary codes and offers a novel characterization of the ternary Golay code.

Findings

t  5 for the design strength

Characterization of the (extended) ternary Golay code

Limits on t-designs in ternary codes

Abstract

Let $C$ be a two and three-weight ternary code. Furthermore, we assume that $C_\ell$ are $t$-designs for all $\ell$ by the Assmus--Mattson theorem. We show that $t \leq 5$. As a corollary, we provide a new characterization of the (extended) ternary Golay code.