1-generator generalized quasi-cyclic codes over \(\mathbb {Z}_{4}\)

1. Aydin, N., Asamov, T.: The \(\mathbb {Z}_{4}\) Database [Online]. Available: http://z4codes.info/. accessed on 28.08.2015

2. Aydin, N., Ray-Chaudhuri, D.K.: Quasi cyclic codes over \(\mathbb {Z}_{4}\) and some new binary codes. IEEE Trans. Inform. Theory 48, 2065–2069 (2009)

   Article  MathSciNet  MATH  Google Scholar 

3. Bosma, W., Cannon, J., Playoust: The Magma algebra system. J. Symb. Comput. 24, 235–265 (1997)

   Article  MathSciNet  MATH  Google Scholar 

4. Cao, Y.: Generalized quasi-cyclic codes over Galois rings: structural properties and enumeration. Appl. Algebra Eng. Commun. Comput. 22, 219–233 (2011)

   Article  MathSciNet  MATH  Google Scholar 

5. Cao, Y.: Structural properties and enumeration of 1-generator generalized quasi-cyclic codes. Des. Codes Cryptogr. 60, 67–79 (2011)

   Article  MathSciNet  MATH  Google Scholar 

6. Esmaeili, M., Yari, S.: Generalized quasi-cyclic codes: Structural properties and codes construction. Appl. Algebra Eng. Commun. Comput. 20, 159–173 (2009)

   Article  MathSciNet  MATH  Google Scholar 

7. Gao, J., Shi, M., Wu, T., Fu, F.-W.: On double cyclic codes over \(\mathbb {Z}_{4}\). arXivpreprint, arXiv:1501.01360v1 (2015)

8. Gao, J., Fu, F.-W., Shen, L., Ren, W.: Some results on generalized quasi-cyclic codes over \(\mathbb {F}_{q}+u\mathbb {F}_{q}\). IEICE Trans. Fundamentals 97, 1005–1011 (2014)

   Article  Google Scholar 

9. Grassl, M.: Table of Bounds on Linear Codes [Online]. Available: http://www.codetables.de/. accessed on 14.05.2015

10. Hammons, J., Kumar, P.V., Calderbank, A.R., Sloane, N.J., Sol é, P.: The \(\mathbb {Z}_{4}\)-linearity of Kerdock, Preparata, Goethals, and related codes. IEEE Trans. Inform. Theory 40(2), 301–319 (1994)

    Article  MathSciNet  MATH  Google Scholar 

11. Van Lint, J.H.: Introduction to Coding Theory. Springer-Verlag, Berlin (1999)

    Book  MATH  Google Scholar 

12. Pless, V., Qian, Z.: Cyclic codes and quadratic residue codes over \(\mathbb {Z}_{4}\). IEEE Trans. Inform. Theory 42, 1594–1600 (1996)

    Article  MathSciNet  MATH  Google Scholar 

13. Siap, I., Abualrub, T., Aydin, N.: Quaternary quasi-cyclic codes with even length components. Ars Combinatoria 101, 425–434 (2011)

    MathSciNet  MATH  Google Scholar 

14. Siap, I., Kulhan, N.: The structure of generalized quasi-cyclic codes. Appl. Math. E-Notes 5, 24–30 (2005)

    MathSciNet  MATH  Google Scholar 

15. Wan, Z.-X.: Quaternary Codes. World Scientific, Singapore (1997)

    Book  MATH  Google Scholar 

Download references