Roberts, Adam2024-08-222024-08-222024-02-22Roberts, A.M. (2024). Self-dual codes from a block matrix construction characterised by group rings. Designs, Codes and Cryptography, 92, 1599–1617. https://doi.org/10.1007/s10623-024-01359-00925-102210.1007/s10623-024-01359-0http://hdl.handle.net/10034/628964This 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/s10623-024-01359-0]This 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/s10623-024-01359-0]We give a new technique for constructing self-dual codes based on a block matrix whose blocks arise from group rings and orthogonal matrices. The technique can be used to construct self-dual codes over finite commutative Frobenius rings of characteristic 2. We give and prove the necessary conditions needed for the technique to produce self-dual codes. We also establish the connection between self-dual codes generated by the new technique and units in group rings. Using the construction together with the building-up construction, we obtain new extremal binary self-dual codes of lengths 64, 66 and 68 and new best known binary self-dual codes of length 80.Attribution-NonCommercial-NoDerivatives 4.0 InternationalBinary self-dual codesGroup ringsGray mapsExtremal codesOptimal codesBest known codesArticle1573-7586Designs, Codes and Cryptography2025-02-2292