LCD Cyclic And Negacyclic Codes Over Z_2^a

Linear complementary dual(LCD)codes are an important class of linear codes which have many applications in data storage communications systems,consumer electronics and cryptography.Recently,LCD codes have been found that there exists an important role in armoring implementations against side-channel attacks and fault injection attacks.This makes the study of LCD codes has become a hot topic in coding theory.This dissertation studies LCD cyclic and negacyclic codes over the finite ring Z2a,gives the generator polynomial of such codes,and constructs two classes of LCD codes over Z4.The main results are listed as follows.(1)A sufficient and necessary condition for cyclic codes over Z2a of odd length to be LCD is given.The generator polynomial of cyclic codes over Z2a of odd length is obtained.It is proved that such codes are free reversible codes.(2)The Hamming distance of the LCD cyclic code C over Z4 of length n=2m+1 with generator polynomial g(x)=(x-1)M12(x)is derived.And such LCD code has Lee distance at least 8.It is proved that the binary image of C is a(2m+1+2,22m+1-4m,?8)binary nonlinear reversible code.(3)The structure and generator polynomial of LCD negacyclic codes over Z4 of even length are determined.It is proved that such codes are free reversible codes.A class of LCD codes with Lee distance is constructed from negacyclic codes over Z4.