\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Long quasi-polycyclic $t-$ CIS codes

Abstract Full Text(HTML) Related Papers Cited by
  • We study complementary information set codes of length $tn$ and dimension $n$ of order $t$ called ($t-$CIS code for short). Quasi-cyclic (QC) and quasi-twisted (QT) $t$-CIS codes are enumerated by using their concatenated structure. Asymptotic existence results are derived for one-generator and fixed co-index QC and QT codes depending on Artin's primitive root conjecture. This shows that there are infinite families of rate $1/t$ long QC and QT $t$-CIS codes with relative distance satisfying a modified Varshamov-Gilbert bound. Similar results are defined for the new and more general class of quasi-polycyclic codes introduced recently by Berger and Amrani.

    Mathematics Subject Classification: 94B60, 12E20.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
  •   A. Alahmadi , C. Güneri , B. Özkaya , H. Shoaib  and  P. Solé , On self-dual double negacirculant codes, Discrete Appl. Math., 222 (2017) , 205-212. 
      A. Alahmadi , S. T. Dougherty , A. Leroy  and  P. Solé , On the duality and the direction of polycyclic codes, Adv. Math. Commun., 10 (2016) , 921--929. 
      N. Aydin  and  D. Ray-Chaudhuri , Quasi-cyclic codes over $\mathbb{Z}_4$ and some new binary codes, IEEE Trans. Inf. Theory, 48 (2002) , 2065-2069. 
      T. P. Berger  and  N. E. Amrani , Codes over finite quotients of polynomial rings, Finite Fields Appl., 25 (2014) , 165-181. 
      W. Bosma , J. Cannon  and  C. Playoust , The Magma algebra system. Ⅰ. The user language, J. Symbolic Comput., 24 (1997) , 235-265. 
      C. Carlet , F. Freibert , S. Guilley , M. Kiermaier , J.-L. Kim  and  P. Solé , Higher-order CIS codes, IEEE Trans. Inf. Theory, 60 (2014) , 5283-5295. 
      C. Carlet , P. Gaborit , J.-L. Kim  and  P. Solé , A new class of codes for Boolean masking of cryptographic computations, IEEE Trans. Inf. Theory, 58 (2012) , 6000-6011. 
      C. L. Chen , W. W. Peterson  and  E. J. Weldon , Some results on quasi-cyclic codes, Inf. Control, 15 (1969) , 407-423. 
      M. Grassl, Tables of Linear Codes and Quantum Codes, available at www.codetables.de
      A. R. Hammons Jr. , P. V. Kumar , A. R. Calderbank , N. J. A. Sloane  and  P. Solé , The $Z_4$ -linearity of Kerdock, Preparata, Goethals and related codes, IEEE Trans. Inf. Theory,, 40 (1994) , 301-319. 
      C. Hooley , On Artin's conjecture, J. Reine Angew. Math., 225 (1967) , 209-220. 
      W. C. Huffman and V. Pless, Fundamentals of Error Correcting Codes, Cambridge Univ. Press, 2003.
      Y. Jia , On quasi-twisted codes over finite fields, Finite Fields Appl., 18 (2012) , 237-257. 
      R. Lidl and H. Niederreiter, Finite Fields, Addison-Wesley, Reading, 1983.
      S. Ling  and  P. Solé , On the algebraic structure of quasi-cyclic codes Ⅰ: finite fields, IEEE Trans. Inf. Theory, 47 (2001) , 2751-2760. 
      P. Moree , Artin's primitive root conjecture--a survey, Integers, 6 (2012) , 1305-1416. 
      Z. -X. Wan, Quaternary Codes, WorldScientific, 1997.
  • 加载中
SHARE

Article Metrics

HTML views(1624) PDF downloads(333) Cited by(0)

Access History

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return