Structure of linear codes invariant under the unitary group $U(3,3)$

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics and Applied Mathematics, Faculty of Science and Agriculture, University of Limpopo, Turfloop, Polokwane, South Africa.

2 School of Mathematical and Statistical Sciences, PAA Focus Area, Faculty of Natural Sciences, North-West University, Mabatho, Mafikeng, South Africa.

Abstract

In this paper, we outline a method for constructing linear codes invariant under primitive permutation groups. We will demonstrate that when a group $G$ possesses a trivial Schur multiplier, every binary linear code that admits $G$ as a permutation group can be regarded as a submodule of the permutation module within the primitive action of $G$. As an illustrative example, we select the finite simple group $G = U(3,3)$ and identify the complete set of linear codes derived from its 2-representations.
In addition, we use the supports of the codewords to construct certain designs that remain invariant under the action of $U(3,3)$ and establish connections between these designs and the corresponding linear codes.

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References

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Algebraic Structures and Their Applications

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Available Online from 18 January 2026

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