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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.
Hossain et al. (Wed,) studied this question.