The present application belongs to the technical field of
information security and
coding theory, and provides a minimal
linear code construction method, a
secret sharing method and a
secret sharing system, comprising: first defining a trace function in a finite field, constructing a two-to-one mapping, a vector
Boolean function with a finite discrete value of Walsh spectrum, and then defining a
code word set based on the function, embedding the output of the trace function into a
linear code generation expression to generate a minimal
linear code with a weight set and a support without strict inclusion; then using the
dual code to establish a one-to-one correspondence between the participants and the
dual code coordinates, the minimal
code word support and the minimum
access structure, embed the secret generation share distribution, and the participants meeting the conditions restore the secret through linear combination. The
system contains four functional modules, which are suitable for distributed storage,
blockchain key management and other scenes, and realize safe, efficient and expandable
secret sharing. The present application can improve the security, efficiency and flexibility of secret sharing, and is suitable for multiple scenes and easy to expand.