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Algebra Appl."],"published-print":{"date-parts":[[2024,6]]},"abstract":"<jats:p> In this work, we analyze the problem of catastrophicity of encoders of convolutional codes over the Laurent series with coefficients in [Formula: see text], [Formula: see text]. Kuijper and Pinto proved in [M.\u00a0Kuijper and R.\u00a0Pinto, On minimality of convolutional ring encoders, IEEE Trans. Autom. Control 55(11) (2009) 4890\u20134897] that, contrary to what happens for codes over [Formula: see text], where [Formula: see text] is a field, when dealing with [Formula: see text] there are convolutional codes that do not admit non-catastrophic encoders. Nevertheless it was conjectured that any catastrophic convolutional code admits another type of non-catastrophic encoder called [Formula: see text]-encoder. In this paper we solve this conjecture for a class of [Formula: see text] convolutional codes over [Formula: see text] and show that, in fact, these codes always admit a non-catastrophic p-encoder. We also describe a constructive procedure that allows us to obtain a non-catastrophic [Formula: see text]-encoder. <\/jats:p>","DOI":"10.1142\/s0219498825500690","type":"journal-article","created":{"date-parts":[[2023,9,21]],"date-time":"2023-09-21T01:46:47Z","timestamp":1695260807000},"source":"Crossref","is-referenced-by-count":0,"title":["On the existence of non-catastrophic p-encoders of (2,1) convolutional codes over \u2124p2"],"prefix":"10.1142","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2303-9824","authenticated-orcid":false,"given":"Diego","family":"Napp","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Alicante, Alicante, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8168-4023","authenticated-orcid":false,"given":"Raquel","family":"Pinto","sequence":"additional","affiliation":[{"name":"CIDMA \u2014 Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, Aveiro, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1701-1817","authenticated-orcid":false,"given":"Concei\u00e7\u00e3o","family":"Rocha","sequence":"additional","affiliation":[{"name":"Instituto Superior de Contabilidade e Administra\u00e7\u00e3o de Coimbra, Instituto Polit\u00e9cnico de Coimbra, Coimbra, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2023,10,14]]},"reference":[{"key":"S0219498825500690BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/BF01390768"},{"key":"S0219498825500690BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2016.01.019"},{"key":"S0219498825500690BIB003","doi-asserted-by":"publisher","DOI":"10.1109\/18.945247"},{"key":"S0219498825500690BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.ffa.2012.09.003"},{"key":"S0219498825500690BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s00200-012-0173-9"},{"key":"S0219498825500690BIB006","series-title":"Prentice Hall Information and System Sciences Series","volume-title":"Linear Systems","author":"Kailath T.","year":"1980"},{"key":"S0219498825500690BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-87448-5_11"},{"issue":"11","key":"S0219498825500690BIB008","first-page":"4890","volume":"55","author":"Kuijper M.","year":"2009","journal-title":"IEEE Trans. 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