On the New Rank Metric Codes Related to Gabidulin Codes

In this paper, we construct a new class of rank metric codes, called <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\lambda$</tex>-twisted Gabidulin codes, and prove some properties of this class of codes. Furthermore, we show an explicit description of the dual of a class of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\lambda$</tex>-twisted Gabidulin codes, which is also applicable to twisted Gabidulin codes. Finally, we explore the application of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\lambda$</tex>-twisted Gabidulin codes in cryptography.