Darafsheh, Mohammad RezaRodrigues, Bernardo GabrielSaeidi, Amin2024-08-212024-08-212023Darafsheh, M.R., Rodrigues, B.G., Saeidi, A. 2023, 'On linear codes constructed from nite groups with a trivial Schur multiplier', Mathematical Communications, vol. 28, no. 1, pp. 85-104.1331-0623 (print)1848-8013 (online)http://hdl.handle.net/2263/97780Using a representation theoretic approach and considering G to be a nite primitive permutation group of degree n with a trivial Schur multiplier, we present a method to determine all binary linear codes of length n that admit G as a permutation automorphism group. In the non-binary case, we can still apply our method, but it will depend on the structure of the stabilizer of a point in the action of G. We show that every binary linear code admitting G as a permutation automorphism group is a submodule of a permutation module de ned by a primitive action of G. As an illustration of the method, we consider G to be the sporadic simple group M11 and construct all binary linear codes invariant under G. We also construct some point- and block-primitive 1-designs from the supports of some codewords of the codes in the discussion and compute their minimum distances, and in many instances we determine the stabilizers of non-zero weight codewords.en© 2023 Department of Mathematics, University of Osijek.Linear codeMathieu groupSchur multiplierTriangular graphArticle