{"id":"https://openalex.org/W4408414838","doi":"https://doi.org/10.3390/sym17030428","title":"Hamming and Symbol-Pair Distances of Constacyclic Codes of Length 2ps over Fpm[u,v]\u27e8u2,v2,uv\u2212vu\u27e9","display_name":"Hamming and Symbol-Pair Distances of Constacyclic Codes of Length 2ps over Fpm[u,v]\u27e8u2,v2,uv\u2212vu\u27e9","publication_year":2025,"publication_date":"2025-03-13","ids":{"openalex":"https://openalex.org/W4408414838","doi":"https://doi.org/10.3390/sym17030428"},"language":"en","primary_location":{"id":"doi:10.3390/sym17030428","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17030428","pdf_url":"https://www.mdpi.com/2073-8994/17/3/428/pdf?version=1741845144","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/17/3/428/pdf?version=1741845144","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111955527","display_name":"D. Acharya","orcid":null},"institutions":[{"id":"https://openalex.org/I164861460","display_name":"Manipal Academy of Higher Education","ror":"https://ror.org/02xzytt36","country_code":"IN","type":"education","lineage":["https://openalex.org/I164861460"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Divya Acharya","raw_affiliation_strings":["Department of Mathematics, Manipal Institute of Technology Bengaluru, Manipal Academy of Higher Education, Manipal 576104, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Manipal Institute of Technology Bengaluru, Manipal Academy of Higher Education, Manipal 576104, India","institution_ids":["https://openalex.org/I164861460"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050272347","display_name":"Prasanna Poojary","orcid":"https://orcid.org/0000-0002-0749-8994"},"institutions":[{"id":"https://openalex.org/I164861460","display_name":"Manipal Academy of Higher Education","ror":"https://ror.org/02xzytt36","country_code":"IN","type":"education","lineage":["https://openalex.org/I164861460"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Prasanna Poojary","raw_affiliation_strings":["Department of Mathematics, Manipal Institute of Technology Bengaluru, Manipal Academy of Higher Education, Manipal 576104, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Manipal Institute of Technology Bengaluru, Manipal Academy of Higher Education, Manipal 576104, India","institution_ids":["https://openalex.org/I164861460"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065724994","display_name":"G. R. Vadiraja Bhatta","orcid":"https://orcid.org/0000-0003-0631-0205"},"institutions":[{"id":"https://openalex.org/I164861460","display_name":"Manipal Academy of Higher Education","ror":"https://ror.org/02xzytt36","country_code":"IN","type":"education","lineage":["https://openalex.org/I164861460"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Vadiraja G. R. Bhatta","raw_affiliation_strings":["Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal 576104, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal 576104, India","institution_ids":["https://openalex.org/I164861460"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5065724994"],"corresponding_institution_ids":["https://openalex.org/I164861460"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02025649,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"3","first_page":"428","last_page":"428"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.6788390278816223},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.6187226176261902},{"id":"https://openalex.org/keywords/symbol","display_name":"Symbol (formal)","score":0.6068459153175354},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4630800187587738},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42557284235954285},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.38491714000701904},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37227118015289307},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34676939249038696},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3327022194862366},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2085759937763214},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.07381138205528259}],"concepts":[{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.6788390278816223},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.6187226176261902},{"id":"https://openalex.org/C134400042","wikidata":"https://www.wikidata.org/wiki/Q2372244","display_name":"Symbol (formal)","level":2,"score":0.6068459153175354},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4630800187587738},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42557284235954285},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.38491714000701904},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37227118015289307},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34676939249038696},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3327022194862366},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2085759937763214},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.07381138205528259},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/sym17030428","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17030428","pdf_url":"https://www.mdpi.com/2073-8994/17/3/428/pdf?version=1741845144","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3390/sym17030428","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17030428","pdf_url":"https://www.mdpi.com/2073-8994/17/3/428/pdf?version=1741845144","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4408414838.pdf"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W91444309","https://openalex.org/W1773531050","https://openalex.org/W1917095352","https://openalex.org/W1995875735","https://openalex.org/W2032505027","https://openalex.org/W2038681062","https://openalex.org/W2039466900","https://openalex.org/W2058283536","https://openalex.org/W2067264852","https://openalex.org/W2092031626","https://openalex.org/W2102759336","https://openalex.org/W2110353549","https://openalex.org/W2129032519","https://openalex.org/W2161496548","https://openalex.org/W2279041544","https://openalex.org/W2328380509","https://openalex.org/W2512704848","https://openalex.org/W2572549162","https://openalex.org/W2735920813","https://openalex.org/W2742653800","https://openalex.org/W2784619229","https://openalex.org/W2792440227","https://openalex.org/W2891359051","https://openalex.org/W2940732945","https://openalex.org/W2955690944","https://openalex.org/W2963311024","https://openalex.org/W2963976753","https://openalex.org/W2977337330","https://openalex.org/W2978042309","https://openalex.org/W3013268251","https://openalex.org/W3013297622","https://openalex.org/W3020002337","https://openalex.org/W3095061981","https://openalex.org/W3151762193","https://openalex.org/W3206558760","https://openalex.org/W4248289108","https://openalex.org/W4249700805","https://openalex.org/W4385823725","https://openalex.org/W4392122428","https://openalex.org/W4399330707","https://openalex.org/W4400760063","https://openalex.org/W4401925461","https://openalex.org/W4402958201"],"related_works":["https://openalex.org/W2943247777","https://openalex.org/W2740543340","https://openalex.org/W2371167013","https://openalex.org/W1493958394","https://openalex.org/W1582340598","https://openalex.org/W2794545997","https://openalex.org/W2584980534","https://openalex.org/W2182731056","https://openalex.org/W1600949677","https://openalex.org/W2779867339"],"abstract_inverted_index":{"Let":[0],"R=Fpm[u,v]\u27e8u2,v2,uv\u2212vu\u27e9,":[1],"where":[2,31],"p":[3],"is":[4,10,33,54,62,108],"an":[5],"odd":[6],"prime":[7],"and":[8,59,92,98,127],"m":[9],"a":[11,15,34,55],"positive":[12,35],"integer.":[13,36],"For":[14],"unit":[16,50],"\u03b1":[17,53],"in":[18,57],"R,":[19],"\u03b1-constacyclic":[20,40,70],"codes":[21,41],"of":[22,29,39,90,112],"length":[23],"2ps":[24],"over":[25],"R":[26,58],"are":[27,42,75,85],"ideals":[28],"R[x]\u27e8x2ps\u2212\u03b1\u27e9,":[30],"s":[32],"The":[37,87],"structure":[38],"classified":[43],"on":[44],"the":[45,49,72,104,109],"distinct":[46],"cases":[47],"for":[48,67],"\u03b1:":[51],"when":[52,60],"square":[56],"it":[61,123],"not.":[63],"In":[64,80],"this":[65,78],"paper,":[66],"all":[68],"such":[69],"codes,":[71],"Hamming":[73,91],"distances":[74,84,94],"determined":[76],"using":[77],"structure.":[79],"addition,":[81],"their":[82,113],"symbol-pair":[83,93],"obtained.":[86],"symmetry":[88,116],"property":[89],"makes":[95],"analysis":[96],"easier":[97],"maintains":[99],"consistency":[100],"by":[101],"guaranteeing":[102],"that":[103],"distance":[105,119],"between":[106],"codewords":[107],"same":[110],"regardless":[111],"order.":[114],"As":[115],"preserves":[117],"invariant":[118],"features":[120],"across":[121],"transformations,":[122],"improves":[124],"error":[125],"detection":[126],"correction.":[128]},"counts_by_year":[],"updated_date":"2025-12-28T23:10:05.387466","created_date":"2025-03-14T00:00:00"}
