F_q-Linear Constacyclic Codes Over F_q^m DFT Approach

Constacyclic codes have good algebraic structure and are easy to be analyzed. Since cyclicity and ease of encoding,constacyclic codes form one of the most important classes of linear codes in coding theory. In this thesis, we mainly study the structure and properties ofFq-linear constacyclic codes on Fqm the finite fields of ordermq. The details are given as follows.First, we obtain the invariant subspaces of Fqm using cyclotomic cosets,subcodes of constacyclic codes by restricting the values of transform component of DFT and then decompose constacyclic codes onFqm.Second, we get the transform domain characteristics of Fq-linear constacyclic codes onFqm.Finally, we find out the dual codes of Fq-linear constacyclic codes, prove the existence of self-dual codes of Fq-linear constacyclic codes, and obtain the parity check matrix and minimal distance of the corresponding QT codes.