2026-09-20T11:36:41Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/50529 2023-07-11 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Duursma, Iwan M. Reznick, Bruce Hajek, Bruce Duursma, Iwan M. Schenck, Henry K. Shen, Jiashun 2014-09-16T17:23:27Z 2014-09-16T17:23:27Z 2014-08 2014-09-16 2014-08 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 i Item withdrawn by Laura Spradlin (lspradl2@illinois.edu) on 2014-07-11T16:40:23Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Shen_Jiashun.pdf: 618067 bytes, checksum: 293e8605860ae3e8b6233f3d34ed71d3 (MD5) Made available in DSpace on 2014-09-16T17:23:27Z (GMT). No. of bitstreams: 2 Jiashun_Shen.pdf: 618067 bytes, checksum: 293e8605860ae3e8b6233f3d34ed71d3 (MD5) license.txt: 4060 bytes, checksum: 4d6014289dd8b9349983a247094d3641 (MD5) http://hdl.handle.net/2142/50529 en Copyright 2014 Jiashun Shen coding theory Reed-Muller codes secret sharing multiparty computation combinatorics multiplicity Multiplicative codes of Reed-Muller type text Mathematics 1257 Mathematics 0439 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Mathematics -UIUC 10KS0439PHD