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J. Found. Comput. Sci."],"published-print":{"date-parts":[[2026,2]]},"abstract":"<jats:p>One-word codes and two-word codes are prefix-suffix-composed codes, then they have a finite completion. There exist n-word codes that have no finite completion when [Formula: see text]. Does every three-word code have a finite completion? Up to now, this famous question in Theory of Codes remains open. In this paper, we construct a series of three-word codes with the form [Formula: see text] that have a finite completion and part of them are prefix-suffix-indecomposable three-word codes.<\/jats:p>","DOI":"10.1142\/s0129054125500091","type":"journal-article","created":{"date-parts":[[2025,3,16]],"date-time":"2025-03-16T22:27:01Z","timestamp":1742164021000},"page":"291-305","source":"Crossref","is-referenced-by-count":0,"title":["Three-Word Codes {a,aba,u} Having a Finite Completion"],"prefix":"10.1142","volume":"37","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-0371-3925","authenticated-orcid":false,"given":"Chunhua","family":"Cao","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Yunnan University, East Outer Ring Road South, University Town, Chenggong District, Kunming 650504, Yunnan Province, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-0254-576X","authenticated-orcid":false,"given":"Zhongmei","family":"Yan","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Yunnan University, East Outer Ring Road South, University Town, Chenggong District, Kunming 650504, Yunnan Province, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-4131-572X","authenticated-orcid":false,"given":"Yali","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Science and Technology, Kunming University of Science, and Technology Oxbridge College, No. 1268 Haiyuan North Road, Kunming 650106, Yunnan Province, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-0723-587X","authenticated-orcid":false,"given":"Hao","family":"Xie","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Yunnan University, East Outer Ring Road South, University Town, Chenggong District, Kunming 650504, Yunnan Province, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-5552-6176","authenticated-orcid":false,"given":"Yingheng","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Yunnan University, East Outer Ring Road South, University Town, Chenggong District, Kunming 650504, Yunnan Province, China"}]}],"member":"219","published-online":{"date-parts":[[2025,3,13]]},"reference":[{"key":"S0129054125500091BIB001","volume-title":"Codes and Automata","author":"Berstel J.","year":"2010"},{"key":"S0129054125500091BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(95)00139-5"},{"key":"S0129054125500091BIB003","doi-asserted-by":"publisher","DOI":"10.1051\/ita\/1989230201351"},{"key":"S0129054125500091BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.ic.2023.105092"},{"key":"S0129054125500091BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.ic.2021.104747"},{"key":"S0129054125500091BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2018.08.022"},{"issue":"4","key":"S0129054125500091BIB007","first-page":"311","volume":"21","author":"Konstantinidis S.","year":"2016","journal-title":"J. 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