Abstract
In this paper, we first introduce Shamir’s construction of the (k; n)-threshold scheme as a typical linear secret-sharing scheme and explain the construction of the (k; l; n)-threshold ramp scheme proposed by Yamamoto and Blakley-Meadows as its extension. Then, by generalizing threshold ramp schemes with a linear code C1 and its subcode C2, we represent a linear secret-sharing scheme in terms of C1 and C2. As examples, we represent Shamir’s (k; n)-threshold scheme and the (k; l; n)-threshold ramp scheme of Yamamoto and Blakley-Meadows using linear codes. Furthermore, we show that in linear secret-sharing schemes, the maximum amount of information leakage of a secret message and their strong security are characterized by the relative generalized Hamming weights (RGHW’s) of C1 and C2 when every share is an element of a finite field.
