Just like prime numbers are to integers, indecomposable codes are to self dual codes. This paper gives an explicit listing of the first few families of binary self dual codes, up to length 16. Binary self dual codes that are decomposable are given as a composition of indecomposable codes. The indecomposable codes are explicitly listed with generator matrices. The complete classifying process is outlined.
","abstract_html":"<p>Just like prime numbers are to integers, indecomposable codes are to self dual codes. This paper gives an explicit listing of the first few families of binary self dual codes, up to length 16. Binary self dual codes that are decomposable are given as a composition of indecomposable codes. The indecomposable codes are explicitly listed with generator matrices. The complete classifying process is outlined. </p>","abstract_has_math":false,"creators":["Russell, Nathan John"],"institution":"Eastern Kentucky University","degree_name":"Master of Arts (MA)","degree_level":"Master's","degree_discipline":"Mathematics and Statistics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-01-01T08:00:00Z","date_published":"2016-01-01T08:00:00Z","updated_at":"2026-07-24T02:15:39Z","subjects":["Binary","Codes","Indecomposable","Self Dual","Mathematics"],"languages":[],"rights":["Copyright 2016 Nathan John Russell"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://encompass.eku.edu/etd/421","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Russell, Nathan John"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["Encompass Digital Archive, Eastern Kentucky University"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics and Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Master's"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Arts (MA)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Eastern Kentucky University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Binary","Codes","Indecomposable","Self Dual","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2016 Nathan John Russell"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://encompass.eku.edu/etd/421"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Just like prime numbers are to integers, indecomposable codes are to self dual codes. This paper gives an explicit listing of the first few families of binary self dual codes, up to length 16. Binary self dual codes that are decomposable are given as a composition of indecomposable codes. The indecomposable codes are explicitly listed with generator matrices. The complete classifying process is outlined.
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"],"dc:format":["application/pdf"],"dc:identifier":["https://encompass.eku.edu/etd/421"],"dc:publisher":["Encompass Digital Archive, Eastern Kentucky University"],"dc:rights":["Copyright 2016 Nathan John Russell"],"dc:source":["Encompass Digital Archive: Online Theses and Dissertations"],"dc:subject":["Binary","Codes","Indecomposable","Self Dual","Mathematics"],"dc:title":["Self Dual Codes and the Indecomposable Building Blocks"],"dc:type":["Master Thesis"],"thesis:degree_discipline":["Mathematics and Statistics"],"thesis:degree_level":["Master's"],"thesis:degree_name":["Master of Arts (MA)"],"thesis:institution_name":["Eastern Kentucky University"]},"updated_at":"2026-07-24T02:15:39Z"}