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A family of repeated-root constacyclic codes over F2+uF2+vF2

  • School of Mathematics, Hefei University of Technology, Hefei 230009, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2014.03.007
  • Received Date: 28 March 2012
  • Accepted Date: 06 July 2012
  • Rev Recd Date: 06 July 2012
  • Publish Date: 30 March 2014
    Abstract

  • Abstract

    The (1+u)-cyclic codes of length 2k over the ring R=F2+uF2+vF2 were studied, and all such codes were classified. A formula for the number of these constacyclic codes was obtained.

    Abstract

    The (1+u)-cyclic codes of length 2k over the ring R=F2+uF2+vF2 were studied, and all such codes were classified. A formula for the number of these constacyclic codes was obtained.
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    • References(13)
  • [1]
    Hammons A R, Kumar P V, Calderbank A R, et al. The Z4-linearity of Kerdock, Preparata, Goethals, and related codes[J]. IEEE Trans Inform Theory，1994，40(2): 301-319.
    [2]
    Calderbank A R, Sloane N J A. Modular and p-adic cyclic codes[J]. Des Codes Crypotogr, 1995, 6(1): 21-35.
    [3]
    Kanwar P, López-Permouth S R. Cyclic codes over the integer modulo pm[J]. Finite Fields Appl, 1997, 3(4): 334-352.
    [4]
    Norton G H, Sǎlǎgean A. On the structure of linear and cyclic codes over finite chain ring[J]. Applicable Algebra in Engineering, Communication and Computing, 2000, 10(6): 489-506.
    [5]
    Dinh H Q, López-Permouth S R. Cyclic and negacyclic codes over finite chain rings[J]. IEEE Trans Inform Theory, 2004, 50(8): 1 728-1 744.
    [6]
    Yildiz B, Karadenniz S. Linear codes over F2+uF2+vF2+uvF2[J]. Des Codes Crypotogr, 2010, 54(1): 61-81.
    [7]
    Yildiz B, Karadenniz S. Cyclic codes over F2+uF2+vF2+uvF2[J]. Des Codes Crypotogr, 2011, 58(3): 221-234.
    [8]
    Castagnoli G, Massey J L, Schoeller P A, et al. On repeated-root cyclic codes[J]. IEEE Trans Inform Theory, 1991, 37(2): 337-342.
    [9]
    Van Lint J H. Repeated-root cyclic codes[J]. IEEE Trans Inform Theory, 1991, 37(2): 343-345.
    [10]
    Abualrub T, Siap I. Constacyclic codes over F2+uF2[J]. J Frank Inst, 2009, 346:520-529.
    [11]
    Abualrub T, Siap I. Cyclic codes over the rings Z2+uZ2 and Z2+uZ2+u2Z2[J]. Des Codes Crypt, 2007, 42(3): 273-287.
    [12]
    Bonnecaze A, Udaya P. Cyclic codes and self-dual codes over F2+uF2[J]. IEEE Trans Inform Theory, 1999, 45(4):1 250-1 255.
    [13]
    Li Ping, Zhu Shixin. Cyclic codes of length 2e over F2+uF2[J]. Journal of Electronics & Information Technology, 2007, 29(5): 1 124-1 126.
    李平，朱士信. 环 F2+uF2上长为2e的循环码[J].电子与信息学报, 2007, 29(5): 1 124-1 126.
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    [1]
    Hammons A R, Kumar P V, Calderbank A R, et al. The Z4-linearity of Kerdock, Preparata, Goethals, and related codes[J]. IEEE Trans Inform Theory，1994，40(2): 301-319.
    [2]
    Calderbank A R, Sloane N J A. Modular and p-adic cyclic codes[J]. Des Codes Crypotogr, 1995, 6(1): 21-35.
    [3]
    Kanwar P, López-Permouth S R. Cyclic codes over the integer modulo pm[J]. Finite Fields Appl, 1997, 3(4): 334-352.
    [4]
    Norton G H, Sǎlǎgean A. On the structure of linear and cyclic codes over finite chain ring[J]. Applicable Algebra in Engineering, Communication and Computing, 2000, 10(6): 489-506.
    [5]
    Dinh H Q, López-Permouth S R. Cyclic and negacyclic codes over finite chain rings[J]. IEEE Trans Inform Theory, 2004, 50(8): 1 728-1 744.
    [6]
    Yildiz B, Karadenniz S. Linear codes over F2+uF2+vF2+uvF2[J]. Des Codes Crypotogr, 2010, 54(1): 61-81.
    [7]
    Yildiz B, Karadenniz S. Cyclic codes over F2+uF2+vF2+uvF2[J]. Des Codes Crypotogr, 2011, 58(3): 221-234.
    [8]
    Castagnoli G, Massey J L, Schoeller P A, et al. On repeated-root cyclic codes[J]. IEEE Trans Inform Theory, 1991, 37(2): 337-342.
    [9]
    Van Lint J H. Repeated-root cyclic codes[J]. IEEE Trans Inform Theory, 1991, 37(2): 343-345.
    [10]
    Abualrub T, Siap I. Constacyclic codes over F2+uF2[J]. J Frank Inst, 2009, 346:520-529.
    [11]
    Abualrub T, Siap I. Cyclic codes over the rings Z2+uZ2 and Z2+uZ2+u2Z2[J]. Des Codes Crypt, 2007, 42(3): 273-287.
    [12]
    Bonnecaze A, Udaya P. Cyclic codes and self-dual codes over F2+uF2[J]. IEEE Trans Inform Theory, 1999, 45(4):1 250-1 255.
    [13]
    Li Ping, Zhu Shixin. Cyclic codes of length 2e over F2+uF2[J]. Journal of Electronics & Information Technology, 2007, 29(5): 1 124-1 126.
    李平，朱士信. 环 F2+uF2上长为2e的循环码[J].电子与信息学报, 2007, 29(5): 1 124-1 126.
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