Secret Sharing Schemes Based on Linear Codes Can Be Precisely Characterized by the Relative Generalized Hamming Weight

@article{Kurihara2012SecretSS,
  title={Secret Sharing Schemes Based on Linear Codes Can Be Precisely Characterized by the Relative Generalized Hamming Weight},
  author={Jun Kurihara and Tomohiko Uyematsu and Ryutaroh Matsumoto},
  journal={IEICE Transactions},
  year={2012},
  volume={95-A},
  pages={2067-2075}
}
This paper precisely characterizes secret sharing schemes based on arbitrary linear codes by using the relative dimension/length profile (RDLP) and the relative generalized Hamming weight (RGHW). We first describe the equivocation Δm of the secret vector s = [s1, . . . ,sl ] given m shares in terms of the RDLP of linear codes. We also characterize two thresholds t1 and t2 in the secret sharing schemes by the RGHW of linear codes. One shows that any set of at most t1 shares leaks no information… CONTINUE READING