{"id":"https://openalex.org/W3172978644","doi":"https://doi.org/10.1109/ieeeconf51394.2020.9443531","title":"A Novel Systematic Representation of Reed-Muller Codes with an Application to Linear Block Feedback Encoding","display_name":"A Novel Systematic Representation of Reed-Muller Codes with an Application to Linear Block Feedback Encoding","publication_year":2020,"publication_date":"2020-11-01","ids":{"openalex":"https://openalex.org/W3172978644","doi":"https://doi.org/10.1109/ieeeconf51394.2020.9443531","mag":"3172978644"},"language":"en","primary_location":{"id":"doi:10.1109/ieeeconf51394.2020.9443531","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ieeeconf51394.2020.9443531","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 54th Asilomar Conference on Signals, Systems, and Computers","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058971371","display_name":"Vinayak Suresh","orcid":"https://orcid.org/0000-0001-7942-5789"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vinayak Suresh","raw_affiliation_strings":["Purdue University,School of Electrical and Computer Engineering","School of Electrical and Computer Engineering, Purdue University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Purdue University,School of Electrical and Computer Engineering","institution_ids":[]},{"raw_affiliation_string":"School of Electrical and Computer Engineering, Purdue University","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001355478","display_name":"David J. Love","orcid":"https://orcid.org/0000-0001-5922-4787"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"David J. Love","raw_affiliation_strings":["Purdue University,School of Electrical and Computer Engineering","School of Electrical and Computer Engineering, Purdue University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Purdue University,School of Electrical and Computer Engineering","institution_ids":[]},{"raw_affiliation_string":"School of Electrical and Computer Engineering, Purdue University","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.24463988,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"677","last_page":"682"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9984999895095825,"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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9983000159263611,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/code-word","display_name":"Code word","score":0.7666735649108887},{"id":"https://openalex.org/keywords/parity-check-matrix","display_name":"Parity-check matrix","score":0.7500094175338745},{"id":"https://openalex.org/keywords/generator-matrix","display_name":"Generator matrix","score":0.6125882863998413},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.5512977242469788},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.5404084920883179},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.5379977226257324},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5130816698074341},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.48020920157432556},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.46372339129447937},{"id":"https://openalex.org/keywords/group-code","display_name":"Group code","score":0.44787436723709106},{"id":"https://openalex.org/keywords/encoder","display_name":"Encoder","score":0.42476311326026917},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4158247411251068},{"id":"https://openalex.org/keywords/encoding","display_name":"Encoding (memory)","score":0.4102901220321655},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.389036625623703},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.365487664937973},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36004990339279175},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35818445682525635}],"concepts":[{"id":"https://openalex.org/C153207627","wikidata":"https://www.wikidata.org/wiki/Q863873","display_name":"Code word","level":3,"score":0.7666735649108887},{"id":"https://openalex.org/C95925971","wikidata":"https://www.wikidata.org/wiki/Q3100414","display_name":"Parity-check matrix","level":4,"score":0.7500094175338745},{"id":"https://openalex.org/C1842014","wikidata":"https://www.wikidata.org/wiki/Q1502046","display_name":"Generator matrix","level":3,"score":0.6125882863998413},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.5512977242469788},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.5404084920883179},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.5379977226257324},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5130816698074341},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.48020920157432556},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.46372339129447937},{"id":"https://openalex.org/C3427991","wikidata":"https://www.wikidata.org/wiki/Q651426","display_name":"Group code","level":5,"score":0.44787436723709106},{"id":"https://openalex.org/C118505674","wikidata":"https://www.wikidata.org/wiki/Q42586063","display_name":"Encoder","level":2,"score":0.42476311326026917},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4158247411251068},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.4102901220321655},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.389036625623703},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.365487664937973},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36004990339279175},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35818445682525635},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ieeeconf51394.2020.9443531","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ieeeconf51394.2020.9443531","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 54th Asilomar Conference on Signals, Systems, and Computers","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1517398983","https://openalex.org/W1545614041","https://openalex.org/W1600838454","https://openalex.org/W1606480398","https://openalex.org/W1975231568","https://openalex.org/W1993003751","https://openalex.org/W2011914761","https://openalex.org/W2040877654","https://openalex.org/W2096307573","https://openalex.org/W2112446888","https://openalex.org/W2113237846","https://openalex.org/W2119257920","https://openalex.org/W2130768170","https://openalex.org/W2150498905","https://openalex.org/W2157875630","https://openalex.org/W2591190829","https://openalex.org/W2964301180","https://openalex.org/W3001795748","https://openalex.org/W3037718443","https://openalex.org/W3175179020"],"related_works":["https://openalex.org/W4247927056","https://openalex.org/W2131338819","https://openalex.org/W3172978644","https://openalex.org/W4237142313","https://openalex.org/W3012554690","https://openalex.org/W4288278449","https://openalex.org/W1579051351","https://openalex.org/W4205411573","https://openalex.org/W2255054582","https://openalex.org/W2966039054"],"abstract_inverted_index":{"Reed-Muller":[0],"(RM)":[1],"codes":[2,10,30,101],"are":[3,78],"an":[4,88,103,155],"important":[5],"and":[6,17,76,82],"powerful":[7],"class":[8],"of":[9,52,59,90,97,125,143,147],"with":[11,110],"several":[12],"applications":[13],"in":[14,46,57],"electrical":[15],"engineering":[16],"computer":[18],"science.":[19],"In":[20],"this":[21,60,91],"work,":[22],"we":[23,93],"prove":[24],"a":[25,35,48,126],"useful":[26],"property":[27,146],"for":[28],"RM":[29,148],"namely":[31],"that":[32],"they":[33,150],"admit":[34],"special":[36],"systematic":[37],"generator":[38],"matrix":[39],"where":[40,74,102],"the":[41,55,67,79,95,111,117,144],"parity":[42],"component":[43],"has":[44],"embedded":[45],"it":[47],"surprisingly":[49],"large":[50,164],"triangle":[51,62],"zeros.":[53],"Asymptotically,":[54],"size":[56],"sub-diagonals":[58],"all-zero":[61],"is":[63,107,120],"shown":[64,121],"to":[65,122,129],"approach":[66],"largest":[68],"possible":[69],"value":[70],"\u2206\u22c6=":[71],"min(K,N":[72],"\u2212K)":[73],"K":[75],"N":[77],"code":[80,83,128],"dimension":[81],"length":[84],"respectively.":[85],"To":[86],"demonstrate":[87],"application":[89],"result,":[92],"introduce":[94],"concept":[96],"linear":[98,159],"block":[99],"feedback":[100,112,160,165],"open":[104],"loop":[105],"codeword":[106],"combined":[108],"linearly":[109],"signal":[113],"during":[114],"encoding":[115,161],"at":[116],"transmitter.":[118],"This":[119],"allow":[123],"strengthening":[124],"weak":[127],"be":[130,152],"as":[131,133],"good":[132],"any":[134],"desired":[135],"code.":[136],"We":[137],"then":[138],"show":[139],"that,":[140],"by":[141],"virtue":[142],"above":[145],"codes,":[149],"can":[151],"emulated":[153],"from":[154],"uncoded":[156],"system":[157],"using":[158],"against":[162],"remarkably":[163],"delays.":[166]},"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
