{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/50529"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/50529","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Multiplicative codes of Reed-Muller type","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","abstract_html":"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","abstract_has_math":false,"creators":["Shen, Jiashun"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Duursma, Iwan M.","Reznick, Bruce","Hajek, Bruce","Schenck, Henry K."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-09-16T17:23:27Z","date_published":"2014-09-16T17:23:27Z","updated_at":"2026-07-22T22:25:40Z","subjects":["coding theory","Reed-Muller codes","secret sharing","multiparty computation","combinatorics","multiplicity"],"languages":["en"],"rights":["Copyright 2014 Jiashun Shen"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/50529","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Duursma, Iwan M.","Reznick, Bruce","Hajek, Bruce","Schenck, Henry K."]},{"key":"dc:creator","label":"Author","values":["Shen, Jiashun"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-09-16T17:23:27Z","2014-08","2014-09-16"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["coding theory","Reed-Muller codes","secret sharing","multiparty computation","combinatorics","multiplicity"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2014 Jiashun Shen"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/50529"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This is a comprehensive study of multiplicative codes of Reed-Muller type and their applications. 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