Enumeration Of Two Classes Of Z₂Z₄-Additive Complementary-Dual Codes

In this thesis, we mainly study necessary and sufficient conditions of Z2Z4-additive codes to be additive complementary-dual codes in two special cases. More-over, we calculate the number of these Z2Z4-additive codes under the condition of permutation equivalence of codes.In Chapter one, we give some background of our research and summarise some known research in these topics. And also, we present the main results of this article. In Chapter two, firstly, we give the basic knowledge about codes, then we present the introduction and explanation of the definition, the generator matrix and duality of Z2Z4-additive codes.Chapter three is the key part of this article, which has three subsections. In Subsection one, we give the definition of Z2Z4-additive complementary-dual codes. In Subsection two, we study necessary and sufficient conditions of Z2Z4-additive codes to be additive complementary-dual codes and calculate the number of these Z2Z4-additive codes under the condition of permutation equivalence. These codes are generated by a non-zero codeword. In last subsection, we study necessary and sufficient conditions of Z2Z4-additive codes to be additive complementary-dual codes and calculate the number of these Z2Z4-additive codes under the condition of per-mutation equivalence of codes. The dimensions of these codes are two and the order of each non-zero codeword is two.Among of our research, when we calculate the number of these Z2Z4-additive complementary-dual codes, firstly, we classify and discuss codewords by the orders of them. Then, we classify and discuss a which is the length of binary part by parity. At last, we calculate the number and get our results.