Transitive and self-dual codes attaining the Tsfasman-Vla˘dut$80-Zink bound

A major problem in coding theory is the question of whether the class of cyclic codes is asymptotically good. In this correspondence-as a generalization of cyclic codes-the notion of transitive codes is introduced (see Definition 1.4 in Section I), and it is shown that the class of transitive codes is asymptotically good. Even more, transitive codes attain the Tsfasman-Vlabrevedut$80-Zink bound over F_q, for all squares q=l². It is also shown that self-orthogonal and self-dual codes attain the Tsfasman-Vlabrevedut$80-Zink bound, thus improving previous results about self-dual codes attaining the Gilbert-Varshamov bound. The main tool is a new asymptotically optimal tower E₀subeE₁ subeE₂sube middotmiddotmiddot of function fields over F_q (with q=lscr²), where all extensions E_n/E₀ are Galois