Nonbinary Quantum Goppa Codes Exceeding the Quantum Gilbert-Varshamov Bound
Quantum Information Processing
Artin automorphisms, cyclotomic function fields, and folded list-decodable codes
Proceedings of the forty-first annual ACM symposium on Theory of computing
A polynomial-time construction of self-orthogonal codes and applications to quantum error correction
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
On the minimal distance of binary self-dual cyclic codes
IEEE Transactions on Information Theory
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Generalization of Steane's enlargement construction of quantum codes and applications
IEEE Transactions on Information Theory
Edge transitive ramanujan graphs and symmetric LDPC good codes
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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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 Fq, 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 Fq (with q=lscr2), where all extensions En/E0 are Galois