# Secret sharing schemes based on additive codes over $GF(4)$

## TL;DR

This paper explores secret sharing schemes based on additive codes over GF(4), highlighting their computational complexity and structural properties, including minimal access structures and connections to generalized 2-designs.

## Contribution

It introduces the study of SSSs based on additive codes over GF(4), detailing their calculation steps and structural features, which were less explored compared to linear code-based schemes.

## Key findings

- Require at least two calculation steps to reveal the secret
- Defined minimal access structures for additive code-based SSSs
- Described SSSs using additive codes containing generalized 2-designs

## Abstract

A secret sharing scheme (SSS) was introduced by Shamir in 1979 using polynomial interpolation. Later it turned out that it is equivalent to an SSS based on a Reed-Solomon code. SSSs based on linear codes have been studied by many researchers. However there is little research on SSSs based on additive codes. In this paper, we study SSSs based on additive codes over $GF(4)$ and show that they require at least two steps of calculations to reveal the secret. We also define minimal access structures of SSSs from additive codes over $GF(4)$ and describe SSSs using some interesting additive codes over $GF(4)$ which contain generalized 2-designs.