Abstract
Linear complementary pair (LCP) of codes and rank metric codes over finite fields have been intensively investigated recently due to their applications in cryptography. In this paper, we first give the definition of LCP of rank-metric codes combined by the LCP of codes and rank-metric codes, and we establish the relationship between LCP of Delsarte codes and LCP of Gabidulin codes. We then present a criterion for Gabidulin codes (C,D) to be LCP. Using this criterion, we obtain two classes of LCP MRD of Gabidulin codes. Finally, we exhibit an interesting application of LCP MRD of Gabidulin codes in coding for the two-user binary adder channel.
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