In this paper, we generalize the vector space construction due to Brickell . This generalization, introduced by Bertilsson , leads to perfect secret sharing schemes with rational information rates in which the secret can be computed efficiently by each qualified group. A one to one correspondence between the generalized construction and linear block codes is stated. It turns out that the approach of minimal codewords by Massey  is a special case of this construction. For general access structures we present an outline of an algorithm for determining whether a rational number can be realized as information rate by means of the generalized vector space construction. If so, the algorithm produces a perfect secret sharing scheme with this information rate. As a side-result we show a correspondence between the duality of access structures and the duality of codes.
|Title of host publication||Advances in Cryptology - EUROCRYPT'94 (Proceedings Workshop on the Theory and Application of Cryptographic Techniques, Perugia, Italy, May 9-12, 1994)|
|Editors||A. Santis, De|
|Place of Publication||Berlin|
|Publication status||Published - 1995|
|Name||Lecture Notes in Computer Science|