One of the questions of current interest in coding theory is the following: given a finite non-solvable permutation group G acting transitively on a set Ω\documentclass[12pt]{minimal}
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\begin{document}$$\Omega $$\end{document}, under what conditions on G are self-dual codes invariant under G existent or nonexistent? In this paper, this problem is investigated under the hypothesis that the group G is an imprimitive rank 3 permutation group. It is proven that if G is an imprimitive rank 3 permutation group acting transitively on the coordinate positions of a self-dual binary code C then G is one of M11\documentclass[12pt]{minimal}
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\begin{document}$${\mathrm{M}}_{11}$$\end{document} of degree 22;Aut(M12)\documentclass[12pt]{minimal}
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\begin{document}$${\mathrm{Aut}}({\mathrm{M}}_{12})$$\end{document} of degree 24; PSL(2,q)\documentclass[12pt]{minimal}
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\begin{document}$$\mathrm{PSL}(2,q)$$\end{document} of degree 2(q+1)\documentclass[12pt]{minimal}
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\begin{document}$$2(q +1)$$\end{document} for q≡1(mod4);\documentclass[12pt]{minimal}
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\begin{document}$$q {\equiv 1}{({\mathrm{mod}}\,4)};$$\end{document}PSL(m,q)\documentclass[12pt]{minimal}
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\begin{document}$$\mathrm{PSL}(m, q)$$\end{document} of degree 2×qm-1q-1\documentclass[12pt]{minimal}
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\begin{document}$$2\times \frac{q^m-1}{q-1}$$\end{document} for m≥3\documentclass[12pt]{minimal}
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\begin{document}$$m \ge 3$$\end{document} odd and q an odd prime; PSL(m,q)\documentclass[12pt]{minimal}
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\begin{document}$$\mathrm{PSL}(m, q)$$\end{document} of degree 2×qm-1q-1\documentclass[12pt]{minimal}
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\begin{document}$$2\times \frac{q^m-1}{q-1}$$\end{document} for m≥4\documentclass[12pt]{minimal}
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\begin{document}$$m \ge 4$$\end{document} even and q an odd prime, and PSL(3,2)\documentclass[12pt]{minimal}
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\begin{document}$$\mathrm{PSL}(3,2)$$\end{document} of degree 14. When combined with a result on the classification of binary self-dual codes invariant under primitive rank 3 permutation groups of almost simple type this yields a result on the non-existence of extremal binary self-dual codes invariant under quasiprimitive rank 3 permutation groups of almost simple type.
