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Codes Cryptogr."],"published-print":{"date-parts":[[2025,7]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>A De Bruijn cycle is a cyclic sequence in which every word of length <jats:italic>n<\/jats:italic> over an alphabet <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\mathcal {A}$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>A<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> appears exactly once. De Bruijn tori are a two-dimensional analogue. Motivated by recent progress on universal partial cycles and words, which shorten De Bruijn cycles using a wildcard character, we introduce universal partial tori and matrices. 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