{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T18:20:45Z","timestamp":1773253245622,"version":"3.50.1"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2021,4,2]],"date-time":"2021-04-02T00:00:00Z","timestamp":1617321600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,4,2]],"date-time":"2021-04-02T00:00:00Z","timestamp":1617321600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["AAECC"],"published-print":{"date-parts":[[2023,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this work, we study codes generated by elements that come from group matrix rings. We present a matrix construction which we use to generate codes in two different ambient spaces: the matrix ring <jats:inline-formula><jats:alternatives><jats:tex-math>$$M_k(R)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:msub>\n                      <mml:mi>M<\/mml:mi>\n                      <mml:mi>k<\/mml:mi>\n                    <\/mml:msub>\n                    <mml:mrow>\n                      <mml:mo>(<\/mml:mo>\n                      <mml:mi>R<\/mml:mi>\n                      <mml:mo>)<\/mml:mo>\n                    <\/mml:mrow>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and the ring <jats:italic>R<\/jats:italic>,\u00a0 where <jats:italic>R<\/jats:italic> is the commutative Frobenius ring. We show that codes over the ring <jats:inline-formula><jats:alternatives><jats:tex-math>$$M_k(R)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:msub>\n                      <mml:mi>M<\/mml:mi>\n                      <mml:mi>k<\/mml:mi>\n                    <\/mml:msub>\n                    <mml:mrow>\n                      <mml:mo>(<\/mml:mo>\n                      <mml:mi>R<\/mml:mi>\n                      <mml:mo>)<\/mml:mo>\n                    <\/mml:mrow>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> are one sided ideals in the group matrix ring <jats:inline-formula><jats:alternatives><jats:tex-math>$$M_k(R)G$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:msub>\n                      <mml:mi>M<\/mml:mi>\n                      <mml:mi>k<\/mml:mi>\n                    <\/mml:msub>\n                    <mml:mrow>\n                      <mml:mo>(<\/mml:mo>\n                      <mml:mi>R<\/mml:mi>\n                      <mml:mo>)<\/mml:mo>\n                    <\/mml:mrow>\n                    <mml:mi>G<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and the corresponding codes over the ring <jats:italic>R<\/jats:italic> are <jats:inline-formula><jats:alternatives><jats:tex-math>$$G^k$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mi>G<\/mml:mi>\n                    <mml:mi>k<\/mml:mi>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-codes of length <jats:italic>kn<\/jats:italic>. Additionally, we give a generator matrix for self-dual codes, which consist of the mentioned above matrix construction. We employ this generator matrix to search for binary self-dual codes with parameters [72,\u00a036,\u00a012] and find new singly-even and doubly-even codes of this type. In particular, we construct 16 new Type\u00a0I and 4 new Type\u00a0II binary [72,\u00a036,\u00a012] self-dual codes.<\/jats:p>","DOI":"10.1007\/s00200-021-00504-9","type":"journal-article","created":{"date-parts":[[2021,4,2]],"date-time":"2021-04-02T12:02:40Z","timestamp":1617364960000},"page":"279-299","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Group matrix ring codes and constructions of self-dual codes"],"prefix":"10.1007","volume":"34","author":[{"given":"S. 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