{"id":{"repo_id":"ecu","oai_identifier":"oai:thescholarship.ecu.edu:10342/8803"},"canonical_url":"https://search.dev.ndltd.org/etd/ecu/oai:thescholarship.ecu.edu:10342/8803","repository":{"repo_id":"ecu","name":"East Carolina University","base_url":"https://thescholarship.ecu.edu/server/oai/request"},"display":{"title":"Studies on Gopala-Hemachandra Codes and their Applications","abstract":"Gopala-Hemachandra codes are a variation of the Fibonacci universal code and have applications in data compression and cryptography. We study a specific parameterization of Gopala-Hemachandra codes and present several results pertaining to these codes. We show that GH_{a}(n) always exists for any n >= 1, when -2 >= a >= -4, meaning that these are universal codes. We develop two new algorithms to determine whether a GH code exists for a given a and n, and to construct them if they exist. We also prove that when a = -(4+k), where k >= 1, that there are at most k consecutive integers for which GH codes do not exist. In 2014, Nalli and Ozyilmaz proposed a stream cipher based on GH codes. We show that this cipher is insecure and provide experimental results on the performance of our program that cracks this cipher.","abstract_html":"Gopala-Hemachandra codes are a variation of the Fibonacci universal code and have applications in data compression and cryptography. We study a specific parameterization of Gopala-Hemachandra codes and present several results pertaining to these codes. We show that GH_{a}(n) always exists for any n >= 1, when -2 >= a >= -4, meaning that these are universal codes. We develop two new algorithms to determine whether a GH code exists for a given a and n, and to construct them if they exist. We also prove that when a = -(4+k), where k >= 1, that there are at most k consecutive integers for which GH codes do not exist. In 2014, Nalli and Ozyilmaz proposed a stream cipher based on GH codes. We show that this cipher is insecure and provide experimental results on the performance of our program that cracks this cipher.","abstract_has_math":false,"creators":["Childers, Logan"],"institution":"East Carolina University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Computer Science","school":null,"contributors":[],"advisors":["Gopalakrishnan, Krishnan"],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-11-16","date_published":"2020-11-16","updated_at":"2026-07-24T02:13:39Z","subjects":["Zeckendorf Representation","Gopala-Hemachandra Codes","Data Compression","Fibonacci Code","Stream Ciphers","Cryptanalysis"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10342/8803","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Gopalakrishnan, Krishnan"]},{"key":"dc:contributor.department","label":"Department","values":["Computer Science"]},{"key":"dc:contributor.other","label":"Dc Contributor Other","values":["Computer Science"]},{"key":"dc:creator","label":"Author","values":["Childers, Logan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2020-12-18T15:48:08Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2020-12-18T15:48:08Z"]},{"key":"dc:date.issued","label":"Date","values":["2020-11-16"]},{"key":"dc:publisher","label":"Institution","values":["East Carolina University"]},{"key":"dc:type","label":"Dc Type","values":["Master's Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Zeckendorf Representation","Gopala-Hemachandra Codes","Data Compression","Fibonacci Code","Stream Ciphers","Cryptanalysis"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10342/8803"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Gopala-Hemachandra codes are a variation of the Fibonacci universal code and have applications in data compression and cryptography. We study a specific parameterization of Gopala-Hemachandra codes and present several results pertaining to these codes. We show that GH_{a}(n) always exists for any n >= 1, when -2 >= a >= -4, meaning that these are universal codes. We develop two new algorithms to determine whether a GH code exists for a given a and n, and to construct them if they exist. We also prove that when a = -(4+k), where k >= 1, that there are at most k consecutive integers for which GH codes do not exist. In 2014, Nalli and Ozyilmaz proposed a stream cipher based on GH codes. We show that this cipher is insecure and provide experimental results on the performance of our program that cracks this cipher."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Studies on Gopala-Hemachandra Codes and their Applications"]}]}],"canonical_facts":{"dc:contributor.advisor":["Gopalakrishnan, Krishnan"],"dc:contributor.department":["Computer Science"],"dc:contributor.other":["Computer Science"],"dc:creator":["Childers, Logan"],"dc:date.accessioned":["2020-12-18T15:48:08Z"],"dc:date.available":["2020-12-18T15:48:08Z"],"dc:date.issued":["2020-11-16"],"dc:description.abstract":["Gopala-Hemachandra codes are a variation of the Fibonacci universal code and have applications in data compression and cryptography. We study a specific parameterization of Gopala-Hemachandra codes and present several results pertaining to these codes. We show that GH_{a}(n) always exists for any n >= 1, when -2 >= a >= -4, meaning that these are universal codes. We develop two new algorithms to determine whether a GH code exists for a given a and n, and to construct them if they exist. We also prove that when a = -(4+k), where k >= 1, that there are at most k consecutive integers for which GH codes do not exist. In 2014, Nalli and Ozyilmaz proposed a stream cipher based on GH codes. We show that this cipher is insecure and provide experimental results on the performance of our program that cracks this cipher."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/10342/8803"],"dc:language.iso":["en"],"dc:publisher":["East Carolina University"],"dc:subject":["Zeckendorf Representation","Gopala-Hemachandra Codes","Data Compression","Fibonacci Code","Stream Ciphers","Cryptanalysis"],"dc:title":["Studies on Gopala-Hemachandra Codes and their Applications"],"dc:type":["Master's Thesis"]},"updated_at":"2026-07-24T02:13:39Z"}