In this paper, we present an isomorphism that connects a code of length [Formula: see text] over [Formula: see text] to a code of length [Formula: see text] over [Formula: see text]. We define criteria for identifying linear complementary pair (LCP) and linear complementary dual (LCD) codes by utilizing this isomorphism. We also introduce the notion of [Formula: see text]-LCP of codes into the LCP framework and give a necessary and sufficient condition for their characterization. We also provide a necessary and sufficient condition for the existence of an maximum distance separable (MDS) [Formula: see text]-LCP of codes. These insights into the structural properties of codes offer promising avenues for their application in various fields, particularly in the realm of finite fields.
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Hossain et al. (2024) studied this question.
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