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On the structure of the linear codes with a given automorphism

The research is partially supported by [the Bulgarian National Science Fund under Contract No KP-06-H62/2/13.12.2022]

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  • The purpose of this paper is to present the structure of the linear codes over a finite field with $ q $ elements that have a permutation automorphism of order $ m $. These codes can be considered as generalized quasi-cyclic codes. Quasi-cyclic codes and almost quasi-cyclic codes are discussed in detail, presenting necessary and sufficient conditions for which linear codes with such an automorphism are self-orthogonal, self-dual, or linear complementary dual.

    Mathematics Subject Classification: Primary: 94B05, 20B25.

    Citation:

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