| A linear code is called a complementary dual linear code(LCD codes in short)if the intersection of and its dual code is zero.Recently,LCD codes have been shown to be important in side channel attacks and have been extensively studied.In particular,many studies have focused on constructing LCD codes that reach the Singleton bound,which are called LCD MDS codes.Linear codes with rank distance is widely used in network and cryptographic algorithm design.In the past ten years,an increasing number of scholars have paid close attention to the rank distance codes,and there are currently substantial research achievements in this field.There are many similar properties between the linear codes that assign rank distance and the linear codes that assign hamming distance.In the case of rank distance,the rank distance codes that reach the Singleton bound is called the MRD codes,and several new types of MRD codes have been constructed in recent years.On this basis,Authors in [5] and [6] have constructed two types of LCD MRD codes respectively based on Gabidulin MRD codes and generalized Gabidulin MRD codes.This paper mainly studies the construction of the new LCD MRD codes:The main results of this thesis are twofold.Firstly,the relationship between the rank distance codes and its dual codes is discussed.With regard to the linearized polynomials and matrices of rank distance codes,it is found that in a group of dual bases,the rank distance codes of these two forms can be guaranteed to have equal inner products under different definitions of inner products.Secondly,a new type of LCD MRD codes is constructed based on generalized Twisted Gabidulin MRD codes in accordance with this relation. |
