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Research has shown that this was remarkably efficient in the case when the code generators are idempotents. In quantum error correction, the theory of stabilizer formalism requires classical self-orthogonal additive codes over the finite field <jats:italic>GF<\/jats:italic>(4), which, via the lens of group algebras, are essentially <jats:inline-formula><jats:alternatives><jats:tex-math>$$F_2$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>F<\/mml:mi>\n                    <mml:mn>2<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-submodules over <jats:italic>GF<\/jats:italic>(4). Therefore, this paper provides a classification on idempotents in commutative group algebra <jats:italic>GF<\/jats:italic>(4)<jats:italic>G<\/jats:italic>, followed by a criterion that allows idempotents to generate stabilizer subgroups. Later, the construction of quantum stabilizer codes is done in the case when <jats:italic>G<\/jats:italic> is a cyclic group <jats:inline-formula><jats:alternatives><jats:tex-math>$$C_n$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>C<\/mml:mi>\n                    <mml:mi>n<\/mml:mi>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, for <jats:inline-formula><jats:alternatives><jats:tex-math>$$n=2^m-1$$<\/jats:tex-math><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:msup>\n                      <mml:mn>2<\/mml:mn>\n                      <mml:mi>m<\/mml:mi>\n                    <\/mml:msup>\n                    <mml:mo>-<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$n=2^m+1$$<\/jats:tex-math><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:msup>\n                      <mml:mn>2<\/mml:mn>\n                      <mml:mi>m<\/mml:mi>\n                    <\/mml:msup>\n                    <mml:mo>+<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. Quantum bounds on their burst error minimum distance are subsequently determined.\n<\/jats:p>","DOI":"10.1007\/s11128-023-03904-7","type":"journal-article","created":{"date-parts":[[2023,3,22]],"date-time":"2023-03-22T14:06:14Z","timestamp":1679493974000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Burst error-correcting quantum stabilizer codes designed from idempotents"],"prefix":"10.1007","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0591-3111","authenticated-orcid":false,"given":"Kai Lin","family":"Ong","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,3,22]]},"reference":[{"issue":"6","key":"3904_CR1","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1007\/BF02650179","volume":"21","author":"R Feynman","year":"1982","unstructured":"Feynman, R.: Simulating physics with computers. 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