Consider ensuring the (k - 1)-th coefficient is non-zero

[psivesely]

Currently there is a (1 / 256) ^ t probability that a secret byte can be recovered with k - t shares. This happens if the a_k-1, a_k-2, ..., a_k-t coefficients are uniformly chosen to be 0. By ensuring the a_k-1 coefficient is non-zero, this probability would be zero.