Multiplicative codes of Reed-Muller type

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

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Shen, Jiashun

Contributors dc:contributor

• Duursma, Iwan M.
• Reznick, Bruce
• Hajek, Bruce
• Schenck, Henry K.

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

Statement dc:rights

• Copyright 2014 Jiashun Shen

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/50529

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/50529