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Let <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\lambda &gt;1$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>\u03bb<\/mml:mi>\n                    <mml:mo>&gt;<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> be a divisor of <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$q-1$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>q<\/mml:mi>\n                    <mml:mo>-<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> and <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\tau &gt;1$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>\u03c4<\/mml:mi>\n                    <mml:mo>&gt;<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> be a divisor of <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$q+1$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>q<\/mml:mi>\n                    <mml:mo>+<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>. Under certain conditions we prove that there exists an MDS stabilizer quantum code with length <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$n=\\lambda \\tau \\sigma $$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>n<\/mml:mi>\n                    <mml:mo>=<\/mml:mo>\n                    <mml:mi>\u03bb<\/mml:mi>\n                    <mml:mi>\u03c4<\/mml:mi>\n                    <mml:mi>\u03c3<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> for a range of values of <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\sigma $$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03c3<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>. This is a flexible construction, which includes previously known families and also new MDS parameters not known before.<\/jats:p>","DOI":"10.1007\/s12095-025-00834-2","type":"journal-article","created":{"date-parts":[[2025,8,13]],"date-time":"2025-08-13T13:49:44Z","timestamp":1755092984000},"page":"1611-1625","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["New quantum MDS codes with flexible parameters from Hermitian self-orthogonal GRS codes"],"prefix":"10.1007","volume":"17","author":[{"given":"Oisin","family":"Campion","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fernando","family":"Hernando","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gary","family":"McGuire","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,8,13]]},"reference":[{"issue":"7779","key":"834_CR1","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1038\/s41586-019-1666-5","volume":"574","author":"F Arute","year":"2019","unstructured":"Arute, F., et al.: Quantum supremacy using a programmable superconducting processor. 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