Roberts, Adam2024-08-222024-08-222022-12-22Roberts, A. M. (2024). Quaternary Hermitian self-dual codes of lengths 26, 32, 36, 38 and 40 from modifications of well-known circulant constructions. Applicable Algebra in Engineering, Communication and Computing, 35, 833–858. https://doi.org/10.1007/s00200-022-00589-w0938-127910.1007/s00200-022-00589-whttp://hdl.handle.net/10034/628963This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s00200-022-00589-w]In this work, we give three new techniques for constructing Hermitian self-dual codes over commutative Frobenius rings with a non-trivial involutory automorphism using λ-circulant matrices. The new constructions are derived as modifications of various well-known circulant constructions of self-dual codes. Applying these constructions together with the building-up construction, we construct many new best known quaternary Hermitian self-dual codes of lengths 26, 32, 36, 38 and 40.Attribution-NonCommercial-NoDerivatives 4.0 InternationalHermitian self-dual codesCodes over ringsλ-circulant matrixOptimal codesBest known codesArticle1432-0622Applicable Algebra in Engineering, Communication and Computing2022-12-2235