{"doi":"10.1002/ecjc.4430770503","title":"A consideration for deriving nonbinary irreducible polynomials","abstract":"<jats:title>Abstract</jats:title><jats:p>An irreducible polynomial can be derived in a stochastic way by examining the irreducibility of randomly generated polynomials. On the other hand, a systematic method of derivation for the irreducible polynomial has recently been introduced by presenting a class of irreducible polynomials of particular forms.</jats:p><jats:p>This paper shows clearly that a higher‐order irreducible polynomial can be derived by applying a suitable variable transformation to the given irreducible polynomial. It is shown also that, when an irreducible polynomial is given where the coefficient is the element of a finite field with odd prime characteristic, an infinite number of higher‐order irreducible polynomials can be derived from that polynomial. A precise algorithm for the derivation is shown.</jats:p>","journal":"Electronics and Communications in Japan (Part III: Fundamental Electronic Science)","year":1994,"id":24222,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":0,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":146086,"name":"Yasunori Suetugu","orcid":null,"position":1,"is_corresponding":false},{"id":146085,"name":"Tatsuo Sugimura","orcid":null,"position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"base_score":0.0,"endowment":0.0,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"18998881","pmcid":null,"openalex_id":"https://openalex.org/W2031091902","authors":[],"funders":[],"total_grants":0,"fwci":0.0,"citation_percentile":0.22371365,"influential_citations":0,"citation_trend":[],"oa_status":"closed","license":"http://onlinelibrary.wiley.com/termsAndConditions#vor","oa_locations":[{"url":"https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1002%2Fecjc.4430770503","host_type":"publisher"},{"url":"https://onlinelibrary.wiley.com/doi/pdf/10.1002/ecjc.4430770503","host_type":"publisher"},{"url":"https://doi.org/10.1002/ecjc.4430770503","host_type":"journal"}],"fields_of_study":["Cryptography and Residue Arithmetic","Coding theory and cryptography","Polynomial and algebraic computation","Mathematics"],"mesh_terms":[],"keywords":["Irreducible polynomial","Mathematics","Irreducibility","Polynomial","Minimal polynomial (linear algebra)","Reciprocal polynomial","Irreducible element","Symmetric polynomial","Matrix polynomial","Factorization of polynomials","Order (exchange)","Stable polynomial","Characteristic polynomial","Pure mathematics","Combinatorics","Discrete mathematics","Alternating polynomial","Mathematical analysis","Fundamental representation"],"sdg_mappings":[],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-06-07T21:53:40.871037Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}