  It is well-known that the linear secret-sharing scheme (LSSS) can be
constructed from linear error-correcting codes (Brickell [1], R.J. McEliece and
D.V.Sarwate [2],Cramer, el.,[3]). The theory of linear codes from
algebraic-geometric curves (algebraic-geometric (AG) codes or geometric Goppa
code) has been well-developed since the work of V.Goppa and Tsfasman, Vladut,
and Zink(see [17], [18] and [19]). In this paper the linear secret-sharing
scheme from algebraic-geometric codes, which are non-threshold scheme for
curves of genus greater than 0, are presented . We analysis the minimal access
structure, $d_{min}$ and $d_{cheat}$([8]), (strongly) multiplicativity and the
applications in verifiable secret-sharing (VSS) scheme and secure multi-party
computation (MPC) of this construction([3] and [10-11]). Our construction also
offers many examples of the self-dually $GF(q)$-representable matroids and many
examples of new ideal linear secret-sharing schemes addressing to the problem
of the characterization of the access structures for ideal secret-sharing
schemes([3] and [9]). The access structures of the linear secret-sharing
schemes from the codes on elliptic curves are given explicitly. From the work
in this paper we can see that the algebraic-geometric structure of the
underlying algebraic curves is an important resource for secret-sharing,
matroid theory, verifiable secret-sharing and secure multi-party computation.
