Secret sharing - Size of the share
In Shamir's secret-sharing scheme, the secret and the shares of the secret all are elements of a finite field, and so necessarily have the same size. In the Reed-Solomon code based variant of Shamir's secret-sharing scheme proposed by the late Bob McEliece and myself (R.J. McEliece and D.V. Sarwate, "On sharing secrets and Reed-Solomon codes", Communications of the ACM, v. 24, Issue 9, Sep 1981), the $n$ shares are $\frac 1k$-th the size of the secret, but these schemes don't have the perfect information-theoretic security of Shamir's scheme. See this answer.