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Cyclic Additive and Quantum Stabilizer Codes

  • Jürgen Bierbrauer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4547)

Abstract

We develop the theory of additive cyclic codes and of cyclic quantum stabilizer codes.

Keywords

Cyclic codes additive codes quantum codes Galois group cyclotomic cosets Kloosterman codes 

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References

  1. 1.
    Ashikhmin, A., Knill, E.: Nonbinary quantum stabilizer codes. IEEE Transactions on Information Theory 47, 3065–3072 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bierbrauer, J.: The theory of cyclic codes and a generalization to additive codes. Designs, Codes and Cryptography 25, 189–206 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bierbrauer, J.: Introduction to Coding Theory, Chapman and Hall/CRC Press, Boca Raton, FL (2004)Google Scholar
  4. 4.
    Bierbrauer, J., Faina, G., Marcugini, S., Pambianco, F.: Additive quaternary codes of small length, Proceedings ACCT, Zvenigorod (Russia) (September 15-18, 2006)Google Scholar
  5. 5.
    Bierbrauer, J., Edel, Y.: Quantum twisted codes. Journal of Combinatorial Designs 8, 174–188 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Blokhuis, A., Brouwer, A.E.: Small additive quaternary codes, European Journal of Combinatorics 25, 161–167 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Calderbank, A.R., Rains, E.M., Shor, P.W., Sloane, N.J.A.: Quantum error correction via codes over GF(4). IEEE Transactions on Information Theory 44, 1369–1387 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Edel, Y., Bierbrauer, J.: Twisted BCH-codes. Journal of Combinatorial Designs 5, 377–389 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Edel, Y., Bierbrauer, J.: Caps of order 3q 2 in affine 4-space in characteristic 2. Finite Fields and Their Applications 10, 168–182 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
  11. 11.
    Rains, E.M.: Nonbinary quantum codes. IEEE Transactions on Information Theory 45, 1827–1832 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Schoof, R., van der Vlugt, M.: Hecke operators and the weight distribution of certain codes. Journal of Combinatorial Theory A 57, 163–186 (1991)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Jürgen Bierbrauer
    • 1
  1. 1.Department of Mathematical Sciences, Michigan Technological University, Houghton, Michigan 49931USA

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