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Multiplicative codes of Reed-Muller type
Shen, Jiashun
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https://hdl.handle.net/2142/50529
Description
- Title
- Multiplicative codes of Reed-Muller type
- Author(s)
- Shen, Jiashun
- Issue Date
- 2014-09-16
- Director of Research (if dissertation) or Advisor (if thesis)
- Duursma, Iwan M.
- Doctoral Committee Chair(s)
- Reznick, Bruce
- Hajek, Bruce
- Committee Member(s)
- Duursma, Iwan M.
- Schenck, Henry K.
- Department of Study
- Mathematics
- Discipline
- Mathematics
- Degree Granting Institution
- University of Illinois at Urbana-Champaign
- Degree Name
- Ph.D.
- Degree Level
- Dissertation
- Date of Ingest
- 2014-09-16T17:23:27Z
- Keyword(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
- Graduation Semester
- 2014-08
- Permalink
- http://hdl.handle.net/2142/50529
- Copyright and License Information
- Copyright 2014 Jiashun Shen
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Graduate Dissertations and Theses at Illinois PRIMARY
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