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Recently, the research of trace codes over finite fields has received a lot of attention because some of these codes have good parameters. In this paper, we construct several classes of trace codes from some special classes of linear codes and give their weight distributions, showing that they contain some optimal and almost optimal codes. Furthermore, we determine the parameters of the duals of the trace codes, and show that they are distance-optimal or nearly distance-optimal with respect to the sphere-packing bound. [ABSTRACT FROM AUTHOR]

In this paper, we give the structures of all ( 1 + u + v ) -constacyclic codes of length 2 s over F 2 + u F 2 + v F 2 + u v F 2 , we also obtain the number of codewords, and the dual of each constacyclic code. Among other results, we study the form of such constacyclic codes that are self-dual and give the number of these codes. We end by giving all self-dual constacyclic codes of length 2, 4 and 8. [ABSTRACT FROM AUTHOR]

In this paper, we explicitly determine the generator polynomials of all repeated-root constacyclic codes of length n l p s over F q and their dual codes, where l is an odd prime different from p , and n is an odd prime different from both l and p such that n = 2 h + 1 for some prime h or h = 1 . Moreover, we give all self-dual cyclic codes of length n l p s over F q and their enumeration. All linear complementary dual (LCD) cyclic codes of length n l p s over F q and their enumeration are also obtained. [ABSTRACT FROM AUTHOR]