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Codes Cryptogr."],"published-print":{"date-parts":[[2024,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We study monomial-Cartesian codes (MCCs) which can be regarded as <jats:inline-formula><jats:alternatives><jats:tex-math>$$(r,\\delta )$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mi>r<\/mml:mi>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mi>\u03b4<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-locally recoverable codes (LRCs). These codes come with a natural bound for their minimum distance and we determine those giving rise to <jats:inline-formula><jats:alternatives><jats:tex-math>$$(r,\\delta )$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mi>r<\/mml:mi>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mi>\u03b4<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-optimal LRCs for that distance, which are in fact <jats:inline-formula><jats:alternatives><jats:tex-math>$$(r,\\delta )$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mi>r<\/mml:mi>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mi>\u03b4<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-optimal. A large subfamily of MCCs admits subfield-subcodes with the same parameters of certain optimal MCCs but over smaller supporting fields. This fact allows us to determine infinitely many sets of new <jats:inline-formula><jats:alternatives><jats:tex-math>$$(r,\\delta )$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mi>r<\/mml:mi>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mi>\u03b4<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-optimal LRCs and their parameters.<\/jats:p>","DOI":"10.1007\/s10623-024-01403-z","type":"journal-article","created":{"date-parts":[[2024,5,2]],"date-time":"2024-05-02T06:01:41Z","timestamp":1714629701000},"page":"2549-2586","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Optimal $$(r,\\delta )$$-LRCs from monomial-Cartesian codes and their subfield-subcodes"],"prefix":"10.1007","volume":"92","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3908-4462","authenticated-orcid":false,"given":"C.","family":"Galindo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9758-2152","authenticated-orcid":false,"given":"F.","family":"Hernando","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6379-6902","authenticated-orcid":false,"given":"H.","family":"Mart\u00edn-Cruz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,5,2]]},"reference":[{"key":"1403_CR1","doi-asserted-by":"publisher","first-page":"39145","DOI":"10.1109\/ACCESS.2022.3165032","volume":"10","author":"B Andrade","year":"2022","unstructured":"Andrade B., Carvalho C., Neumann V.G.L., Veiga A.C.P.: A family of codes with locality containing optimal codes. 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