Quantum cyclic and constacyclic codes

Based on classical quaternary constacyclic linear codes, we construct a set of quantum codes with parameters [[(4/sup m/ -1)/3, (4/sup m/ -1)/3 -2(3l + b)m, 4l + b + 2]] where m/spl ges/4, 1/spl les/b/spl les/3, and 12l + 3b < 2 /spl times/ 4/sup /spl lfloor/(m+2)/3/spl rfloor//-1, which are better than the codes in Bierbrauer and Edel (2000).

[1]  Y. Edel,et al.  Quantum twisted codes , 2000 .

[2]  S. Litsyn,et al.  On binary constructions of quantum codes , 1998, Proceedings of the 1999 IEEE Information Theory and Communications Workshop (Cat. No. 99EX253).

[3]  Andrew M. Steane.  Enlargement of Calderbank-Shor-Steane quantum codes , 1999, IEEE Trans. Inf. Theory.

[4]  Vassil Y. Yorgov.  A method for constructing inequivalent self-dual codes with applications to length 56 , 1987, IEEE Trans. Inf. Theory.

[5]  Andrew M. Steane.  Quantum Reed-Muller codes , 1999, IEEE Trans. Inf. Theory.

[6]  N. Sloane,et al.  Quantum error correction via codes over GF(4) , 1996, Proceedings of IEEE International Symposium on Information Theory.

[7]  I. Fuss,et al.  Quantum Reed-Muller codes , 1997, quant-ph/9703045.