Multiplicative codes of Reed-Muller type

coding theory;Reed-Muller codes;secret sharing;multiparty computation;combinatorics;multiplicity

Shen, Jiashun

关键词: coding theory;    Reed-Muller codes;    secret sharing;    multiparty computation;    combinatorics;    multiplicity;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/50529/Jiashun_Shen.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

This is a comprehensive study of multiplicative codes of Reed-Muller type and their applications.Our codes apply to theelds of cryptography and coding theory, especially to multiparty computa-tion and secret sharing schemes. We also study the AB method to analyze the minimum distanceof linear codes. The multiplicative codes of Reed-Muller type and the AB method are connectedwhen we study the distance and dual distance of a code and its square. Generator matrices for ourcodes use a combination of blocks, where a block consists of all columns of a given weight. Severalinteresting linear codes, which are best known linear codes for a given length and dimension, canbe constructed in this way.i