리드-뮬러 부호의 일반화된 해밍 무게

Abstract

The Reed-Muller codes are one of the best known error correcting codes. The Reed-Muller codes are used to create secret sharing schemes. It is effective to use the generalized Hamming weights of the error correction codes to analyze the access structure of the secret sharing schemes. The generalized Hamming weights are a generalization of the minimum distance of the error correction codes. In this thesis, we obtain lower bounds of the generalized Hamming weights of Reed-Muller codes based on the theory of the Groebner basis. It turns out that the values we obtain are true generalized Hamming weights of the Reed-Muller codes. To obtain these result we first summarize the basic theory and concepts of Reed-Muller codes.