{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:53:33Z","timestamp":1760144013089,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,3,15]],"date-time":"2024-03-15T00:00:00Z","timestamp":1710460800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Portuguese Foundation for Science and Technology (FCT\u2014Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia)","doi-asserted-by":"publisher","award":["UIDB\/04106\/2020","UIDP\/04106\/2020"],"award-info":[{"award-number":["UIDB\/04106\/2020","UIDP\/04106\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In general, the problem of building optimal convolutional codes under a certain criteria is hard, especially when size field restrictions are applied. In this paper, we confront the challenge of constructing an optimal 2D convolutional code when communicating over an erasure channel. We propose a general construction method for these codes. Specifically, we provide an optimal construction where the decoding method presented in the bibliography is considered.<\/jats:p>","DOI":"10.3390\/axioms13030197","type":"journal-article","created":{"date-parts":[[2024,3,15]],"date-time":"2024-03-15T09:32:30Z","timestamp":1710495150000},"page":"197","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Optimal Construction for Decoding 2D Convolutional Codes over an Erasure Channel"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8168-4023","authenticated-orcid":false,"given":"Raquel","family":"Pinto","sequence":"first","affiliation":[{"name":"CIDMA\u2014Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0423-9310","authenticated-orcid":false,"given":"Marcos","family":"Spreafico","sequence":"additional","affiliation":[{"name":"INMA\u2014Institute of Mathematics, Federal University of Mato Grosso do Sul, Campo Grande 79070-900, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3362-8817","authenticated-orcid":false,"given":"Carlos","family":"Vela","sequence":"additional","affiliation":[{"name":"CIDMA\u2014Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1068","DOI":"10.1109\/18.335967","article-title":"Algebraic aspects of two-dimensional convolutional codes","volume":"40","author":"Fornasini","year":"1994","journal-title":"IEEE Trans. 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