Strongly-secure secret sharing based on linear codes can be characterized by generalized hamming weight

Secret sharing scheme is an important tool for the management of secret information. For secret sharing scheme based on linear block codes, the amount of information leaked to adversaries has not been investigated. Hence, in existing constructions of secret sharing scheme based on arbitrary linear codes, some elements of a secret vector s⃗ = [s₁,..., s_l] might leak out deterministically from a non-qualified set. In this paper, we first define anti-access set J as a special non-qualified set. For J, no information about every (t + 1)-tuple of s₁,..., s_l leaks out from any subset of J with cardinality |J|-t. We also introduce the conditions of a linear code and its dual code such that a specified set becomes an anti-access set in secret sharing scheme using the code. Then, we propose a secret sharing scheme based on a linear code C. The proposed secret sharing scheme realizes a similar access structure to threshold access structures, and every non-qualified set whose cardinality is less than or equal to a are anti-access sets. Further, we show that the proposed scheme can be completely characterized by the generalized Hamming weight of C^⊥.