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On the practical side, using birthday techniques known for , we present two algorithms: a probabilistic algorithm for  running in time <jats:inline-formula><jats:alternatives><jats:tex-math>$$q^{\\frac{2}{3}(n+m)}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mi>q<\/mml:mi>\n                    <mml:mrow>\n                      <mml:mfrac>\n                        <mml:mn>2<\/mml:mn>\n                        <mml:mn>3<\/mml:mn>\n                      <\/mml:mfrac>\n                      <mml:mrow>\n                        <mml:mo>(<\/mml:mo>\n                        <mml:mi>n<\/mml:mi>\n                        <mml:mo>+<\/mml:mo>\n                        <mml:mi>m<\/mml:mi>\n                        <mml:mo>)<\/mml:mo>\n                      <\/mml:mrow>\n                    <\/mml:mrow>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> up to a polynomial factor, and a deterministic algorithm for  with roots, running in time <jats:inline-formula><jats:alternatives><jats:tex-math>$$q^{\\min \\{m,n,k\\}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mi>q<\/mml:mi>\n                    <mml:mrow>\n                      <mml:mo>min<\/mml:mo>\n                      <mml:mo>{<\/mml:mo>\n                      <mml:mi>m<\/mml:mi>\n                      <mml:mo>,<\/mml:mo>\n                      <mml:mi>n<\/mml:mi>\n                      <mml:mo>,<\/mml:mo>\n                      <mml:mi>k<\/mml:mi>\n                      <mml:mo>}<\/mml:mo>\n                    <\/mml:mrow>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> up to a polynomial factor. Lastly, to confirm these findings, we solve randomly-generated instances of  using these two algorithms.<\/jats:p>","DOI":"10.1007\/s10623-023-01338-x","type":"journal-article","created":{"date-parts":[[2024,1,8]],"date-time":"2024-01-08T13:02:21Z","timestamp":1704718941000},"page":"833-862","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Hardness estimates of the code equivalence problem in the rank metric"],"prefix":"10.1007","volume":"92","author":[{"given":"Krijn","family":"Reijnders","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Simona","family":"Samardjiska","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Monika","family":"Trimoska","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,1,8]]},"reference":[{"key":"1338_CR1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ffa.2022.102013","volume":"80","author":"GN Alfarano","year":"2022","unstructured":"Alfarano G.N., Lobillo F.J., Neri A., Wachter-Zeh A.: Sum-rank product codes and bounds on the minimum distance. 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