The local leakage-resilience conjecture for Massey schemes

Let $C$ be an MDS code over a prime field $\mathbb{F}_p$, and let the Massey scheme be the secret-sharing scheme defined by $C$. A scheme is one-bit local leakage resilient if it remains secure when each participant reveals one bit of locally computed leakage; its rate is the ratio of the secret length to the total share length. The local leakage-resilience conjecture. The Massey scheme defined with $C$ is one-bit local leakage resilient for any positive rate. This conjecture is the main conjecture in local leakage resilience and was first stated for Shamir's scheme. The supplied text gives no resolution status for the prime-field statement, so its status is recorded as open.