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Title:Multiplicative codes of Reed-Muller type
Author(s):Shen, Jiashun
Director of Research:Duursma, Iwan M.
Doctoral Committee Chair(s):Reznick, Bruce; Hajek, Bruce
Doctoral Committee Member(s):Duursma, Iwan M.; Schenck, Henry K.
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):coding theory
Reed-Muller codes
secret sharing
multiparty computation
combinatorics
multiplicity
Abstract:This is a comprehensive study of multiplicative codes of Reed-Muller type and their applications. Our codes apply to the elds of cryptography and coding theory, especially to multiparty computa- tion and secret sharing schemes. We also study the AB method to analyze the minimum distance of linear codes. The multiplicative codes of Reed-Muller type and the AB method are connected when we study the distance and dual distance of a code and its square. Generator matrices for our codes use a combination of blocks, where a block consists of all columns of a given weight. Several interesting linear codes, which are best known linear codes for a given length and dimension, can be constructed in this way. i
Issue Date:2014-09-16
URI:http://hdl.handle.net/2142/50529
Rights Information:Copyright 2014 Jiashun Shen
Date Available in IDEALS:2014-09-16
Date Deposited:2014-08


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