{"id":{"repo_id":"southwales","oai_identifier":"oai:pure.atira.dk:studenttheses/b359130e-bfc2-4df0-a6f5-55879212010d"},"canonical_url":"https://search.dev.ndltd.org/etd/southwales/oai:pure.atira.dk:studenttheses/b359130e-bfc2-4df0-a6f5-55879212010d","repository":{"repo_id":"southwales","name":"University of South Wales","base_url":"https://pure.southwales.ac.uk/ws/oai"},"display":{"title":"Erasure-Correcting Codes Derived From Sudoku &amp; Related Combinatorial Structures","abstract":"This thesis presents the results of an investigation into the use of puzzle-based combinatorial structures for erasure correction purposes. The research encompasses two main combinatorial structures: the well-known number placement puzzle Sudoku and a novel three component construction designed specifically with puzzle-based erasure correction in mind. The thesis describes the construction of outline erasure correction schemes incorporating each of the two structures.<br/><br/>The research identifies that both of the structures contain a number of smaller sub-structures, the removal of which results in a grid with more than one potential solution - a detrimental property for erasure correction purposes. Extensive investigation into the properties of these sub-structures is carried out for each of the two outline erasure correction schemes, and results are determined that indicate that, although the schemes are theoretically feasible, the prevalence of sub-structures results in practically infeasible schemes.<br/><br/>The thesis presents detailed classifications for the different cases of sub-structures observed in each of the outline erasure correction schemes. The anticipated similarities in the sub-structures of Sudoku and sub-structures of Latin Squares, an established area of combinatorial research, are observed and investigated, the proportion of Sudoku puzzles free of small sub-structures is calculated and a simulation comparing the recovery rates of small sub-structure free Sudoku and standard Sudoku is carried out. The analysis of sub-structures for the second erasure correction scheme involves detailed classification of a variety of small sub-structures; the thesis also derives probabilistic lower bounds for the expected numbers of case-specific sub-structures within the puzzle structure, indicating that specific types of sub-structure hinder recovery to such an extent that the scheme is infeasible for practical erasure correction.<br/><br/>The consequences of complex cell inter-relationships and wider issues with puzzle-based erasure correction, beyond the structures investigated in the thesis are also discussed, concluding that while there are suggestions in the literature that Sudoku and other puzzle-based combinatorial structures may be useful for erasure correction, the work of this thesis suggests that this is not the case.","abstract_html":"This thesis presents the results of an investigation into the use of puzzle-based combinatorial structures for erasure correction purposes. The research encompasses two main combinatorial structures: the well-known number placement puzzle Sudoku and a novel three component construction designed specifically with puzzle-based erasure correction in mind. The thesis describes the construction of outline erasure correction schemes incorporating each of the two structures.&lt;br/&gt;&lt;br/&gt;The research identifies that both of the structures contain a number of smaller sub-structures, the removal of which results in a grid with more than one potential solution - a detrimental property for erasure correction purposes. Extensive investigation into the properties of these sub-structures is carried out for each of the two outline erasure correction schemes, and results are determined that indicate that, although the schemes are theoretically feasible, the prevalence of sub-structures results in practically infeasible schemes.&lt;br/&gt;&lt;br/&gt;The thesis presents detailed classifications for the different cases of sub-structures observed in each of the outline erasure correction schemes. The anticipated similarities in the sub-structures of Sudoku and sub-structures of Latin Squares, an established area of combinatorial research, are observed and investigated, the proportion of Sudoku puzzles free of small sub-structures is calculated and a simulation comparing the recovery rates of small sub-structure free Sudoku and standard Sudoku is carried out. The analysis of sub-structures for the second erasure correction scheme involves detailed classification of a variety of small sub-structures; the thesis also derives probabilistic lower bounds for the expected numbers of case-specific sub-structures within the puzzle structure, indicating that specific types of sub-structure hinder recovery to such an extent that the scheme is infeasible for practical erasure correction.&lt;br/&gt;&lt;br/&gt;The consequences of complex cell inter-relationships and wider issues with puzzle-based erasure correction, beyond the structures investigated in the thesis are also discussed, concluding that while there are suggestions in the literature that Sudoku and other puzzle-based combinatorial structures may be useful for erasure correction, the work of this thesis suggests that this is not the case.","abstract_has_math":false,"creators":["Phillips, Linzy"],"institution":null,"degree_name":"Doctoral Thesis","degree_level":"Student thesis","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Perkins, Stephanie","Roach, Paul"],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-2-21","date_published":"2013-2-21","updated_at":"2026-07-24T04:39:05Z","subjects":["Comninatorial analysis Set theory"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["oai:pure.atira.dk:studenttheses/b359130e-bfc2-4df0-a6f5-55879212010d"],"render_values":[{"text":"oai:pure.atira.dk:studenttheses/b359130e-bfc2-4df0-a6f5-55879212010d","href":null,"code":true}]}]},"links":{"outbound_url":"https://pure.southwales.ac.uk/en/studentTheses/b359130e-bfc2-4df0-a6f5-55879212010d","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Perkins, Stephanie","Roach, Paul"]},{"key":"dc:creator","label":"Author","values":["Phillips, Linzy"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2013-2-21"]},{"key":"dc:date.issued","label":"Date","values":["2013-2-21"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["https://pure.southwales.ac.uk/en/studentTheses/b359130e-bfc2-4df0-a6f5-55879212010d"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Student thesis"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["Doctoral Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Comninatorial analysis Set theory"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["oai:pure.atira.dk:studenttheses/b359130e-bfc2-4df0-a6f5-55879212010d","https://pure.southwales.ac.uk/en/studentTheses/b359130e-bfc2-4df0-a6f5-55879212010d"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://pure.southwales.ac.uk/files/2652347/L_A_Phillips_2013_2059718.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis presents the results of an investigation into the use of puzzle-based combinatorial structures for erasure correction purposes. The research encompasses two main combinatorial structures: the well-known number placement puzzle Sudoku and a novel three component construction designed specifically with puzzle-based erasure correction in mind. The thesis describes the construction of outline erasure correction schemes incorporating each of the two structures.<br/><br/>The research identifies that both of the structures contain a number of smaller sub-structures, the removal of which results in a grid with more than one potential solution - a detrimental property for erasure correction purposes. Extensive investigation into the properties of these sub-structures is carried out for each of the two outline erasure correction schemes, and results are determined that indicate that, although the schemes are theoretically feasible, the prevalence of sub-structures results in practically infeasible schemes.<br/><br/>The thesis presents detailed classifications for the different cases of sub-structures observed in each of the outline erasure correction schemes. The anticipated similarities in the sub-structures of Sudoku and sub-structures of Latin Squares, an established area of combinatorial research, are observed and investigated, the proportion of Sudoku puzzles free of small sub-structures is calculated and a simulation comparing the recovery rates of small sub-structure free Sudoku and standard Sudoku is carried out. The analysis of sub-structures for the second erasure correction scheme involves detailed classification of a variety of small sub-structures; the thesis also derives probabilistic lower bounds for the expected numbers of case-specific sub-structures within the puzzle structure, indicating that specific types of sub-structure hinder recovery to such an extent that the scheme is infeasible for practical erasure correction.<br/><br/>The consequences of complex cell inter-relationships and wider issues with puzzle-based erasure correction, beyond the structures investigated in the thesis are also discussed, concluding that while there are suggestions in the literature that Sudoku and other puzzle-based combinatorial structures may be useful for erasure correction, the work of this thesis suggests that this is not the case."]},{"key":"dc:title","label":"Title","values":["Erasure-Correcting Codes Derived From Sudoku &amp; Related Combinatorial Structures"]}]}],"canonical_facts":{"dc:contributor.advisor":["Perkins, Stephanie","Roach, Paul"],"dc:creator":["Phillips, Linzy"],"dc:date":["2013-2-21"],"dc:date.issued":["2013-2-21"],"dc:description.abstract":["This thesis presents the results of an investigation into the use of puzzle-based combinatorial structures for erasure correction purposes. The research encompasses two main combinatorial structures: the well-known number placement puzzle Sudoku and a novel three component construction designed specifically with puzzle-based erasure correction in mind. The thesis describes the construction of outline erasure correction schemes incorporating each of the two structures.<br/><br/>The research identifies that both of the structures contain a number of smaller sub-structures, the removal of which results in a grid with more than one potential solution - a detrimental property for erasure correction purposes. Extensive investigation into the properties of these sub-structures is carried out for each of the two outline erasure correction schemes, and results are determined that indicate that, although the schemes are theoretically feasible, the prevalence of sub-structures results in practically infeasible schemes.<br/><br/>The thesis presents detailed classifications for the different cases of sub-structures observed in each of the outline erasure correction schemes. The anticipated similarities in the sub-structures of Sudoku and sub-structures of Latin Squares, an established area of combinatorial research, are observed and investigated, the proportion of Sudoku puzzles free of small sub-structures is calculated and a simulation comparing the recovery rates of small sub-structure free Sudoku and standard Sudoku is carried out. The analysis of sub-structures for the second erasure correction scheme involves detailed classification of a variety of small sub-structures; the thesis also derives probabilistic lower bounds for the expected numbers of case-specific sub-structures within the puzzle structure, indicating that specific types of sub-structure hinder recovery to such an extent that the scheme is infeasible for practical erasure correction.<br/><br/>The consequences of complex cell inter-relationships and wider issues with puzzle-based erasure correction, beyond the structures investigated in the thesis are also discussed, concluding that while there are suggestions in the literature that Sudoku and other puzzle-based combinatorial structures may be useful for erasure correction, the work of this thesis suggests that this is not the case."],"dc:identifier":["oai:pure.atira.dk:studenttheses/b359130e-bfc2-4df0-a6f5-55879212010d","https://pure.southwales.ac.uk/en/studentTheses/b359130e-bfc2-4df0-a6f5-55879212010d"],"dc:identifier.uri":["https://pure.southwales.ac.uk/files/2652347/L_A_Phillips_2013_2059718.pdf"],"dc:language":["eng"],"dc:relation.isreferencedby":["https://pure.southwales.ac.uk/en/studentTheses/b359130e-bfc2-4df0-a6f5-55879212010d"],"dc:subject":["Comninatorial analysis Set theory"],"dc:title":["Erasure-Correcting Codes Derived From Sudoku &amp; Related Combinatorial Structures"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["Student thesis"],"dc:type.qualificationname":["Doctoral Thesis"]},"updated_at":"2026-07-24T04:39:05Z"}