ISSN 0253-2778

CN 34-1054/N

open
Free to Publish. Free to Read.
Open AccessOpen Access JUSTC Original Paper

Constacyclic codes over Rk

  • 1.

    School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241003, China

  • 2.

    School of Mathematics, Hefei University of Technology, Hefei 23009, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2014.03.006
  • Received Date: 18 May 2012
  • Accepted Date: 26 August 2012
  • Rev Recd Date: 26 August 2012
  • Publish Date: 30 March 2014
    Abstract

  • Abstract

    Constacyclic codes over Rk were mainly discussed. It was proved that the image of a (1+uk)-constacyclic code of length n over Rk  under  is a binary quasi-cyclic of index 2k-1 and length 2kn. Rk[x]/(xn-(1+uk)) ring was studied. It was obtained that Rk,n is local when n=2m, that Rk,n is not local when n=2ms, where s>1 is an odd number.

    Abstract

    Constacyclic codes over Rk were mainly discussed. It was proved that the image of a (1+uk)-constacyclic code of length n over Rk  under  is a binary quasi-cyclic of index 2k-1 and length 2kn. Rk[x]/(xn-(1+uk)) ring was studied. It was obtained that Rk,n is local when n=2m, that Rk,n is not local when n=2ms, where s>1 is an odd number.
    • FullText(HTML)
  • loading
    • References(11)
  • [1]
    Nechaev A A. Kerdock codes in cyclic form[J]. Dis Math Appl, 1991, 1(4):365-384.
    [2]
    Hammons A R. The Z4-linearity of Kerdock, Preparata, Goethals, and related codes[J]. IEEE Trans Inform Theory, 1994, 40(2):301-319.
    [3]
    Blackford T. Negacyclic codes over Z4 of even length[J]. IEEE Trans Inform Theory, 2003, 49(6):1 417-1 424.
    [4]
    Zhu S, Kai X. Dual and self-dual negacyclic codes of even length over Z2a[J]. Dis Math, 2009, 308:2 382-2 391.
    [5]
    Dinh H Q. Negacyclic codes of even length 2s over Galois rings[J]. IEEE Trans Inform Theory, 2005, 51(12):4 252-4 262.
    [6]
    Dinh H Q, López-permauth S R. Cyclic and negacyclic codes over finite chain rings[J]. IEEE Trans Inform Theory, 2004, 50(8):1 728-1 744.
    [7]
    Li Ping, Zhu Shixin. Cyclic codes of arbitrary lengths over the ring Fq+uFq[J]. Journal of University of Science and Technology of China，2008, 38(12):1 392-1 396.
    李平,朱士信. 环Fq+uFq上任意长度的循环码[J].中国科学技术大学学报，2008, 38(12):1 392-1 396.
    [8]
    Zhu S, Kai X. Negacyclic codes over Galois rings of characteristic 2a[J]. Sci China Math, 2012, 55(4):869-879.
    [9]
    Yildiz B, Karadeniz S. Linear codes over F2+uF2+vF2+uvF2[J]. Des Codes Cryptogr, 2010, 54(1):61-81.
    [10]
    Dougherth S T, Yildiz B, Karadeniz S. Codes over Rk, Gray maps and their binary images[J]. Finite Fields and Their Applications, 2011, 17:205-219.
    [11]
    Dougherth S T, Yildiz B. Karadeniz S. Cyclic codes over Rk[J]. Des Codes Cryptogr, 2012, 63(1):113-126.
    • Supplements(0)
    • Related Articles
    • Track Citations
  • 加载中

Catalog

    |
    Get Citation
    PDF
    XML
    [1]
    Nechaev A A. Kerdock codes in cyclic form[J]. Dis Math Appl, 1991, 1(4):365-384.
    [2]
    Hammons A R. The Z4-linearity of Kerdock, Preparata, Goethals, and related codes[J]. IEEE Trans Inform Theory, 1994, 40(2):301-319.
    [3]
    Blackford T. Negacyclic codes over Z4 of even length[J]. IEEE Trans Inform Theory, 2003, 49(6):1 417-1 424.
    [4]
    Zhu S, Kai X. Dual and self-dual negacyclic codes of even length over Z2a[J]. Dis Math, 2009, 308:2 382-2 391.
    [5]
    Dinh H Q. Negacyclic codes of even length 2s over Galois rings[J]. IEEE Trans Inform Theory, 2005, 51(12):4 252-4 262.
    [6]
    Dinh H Q, López-permauth S R. Cyclic and negacyclic codes over finite chain rings[J]. IEEE Trans Inform Theory, 2004, 50(8):1 728-1 744.
    [7]
    Li Ping, Zhu Shixin. Cyclic codes of arbitrary lengths over the ring Fq+uFq[J]. Journal of University of Science and Technology of China，2008, 38(12):1 392-1 396.
    李平,朱士信. 环Fq+uFq上任意长度的循环码[J].中国科学技术大学学报，2008, 38(12):1 392-1 396.
    [8]
    Zhu S, Kai X. Negacyclic codes over Galois rings of characteristic 2a[J]. Sci China Math, 2012, 55(4):869-879.
    [9]
    Yildiz B, Karadeniz S. Linear codes over F2+uF2+vF2+uvF2[J]. Des Codes Cryptogr, 2010, 54(1):61-81.
    [10]
    Dougherth S T, Yildiz B, Karadeniz S. Codes over Rk, Gray maps and their binary images[J]. Finite Fields and Their Applications, 2011, 17:205-219.
    [11]
    Dougherth S T, Yildiz B. Karadeniz S. Cyclic codes over Rk[J]. Des Codes Cryptogr, 2012, 63(1):113-126.
    Recommended articles
    TrendMD
    Volume 44 Issue 3 page: 203-206
    Cover

    Article Metrics

    Article views (35) PDF downloads(71)
    Proportional views

    Copyright © Editorial Office of JUSTC, All Rights Reserved. 皖ICP备05002528号

    Supported by: Beijing Renhe Information Technology Co. Ltd    

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return