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Existence conditions for self-orthogonal negacyclic codes over finite fields

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  • In this paper, we obtain necessary and sufficient conditions for the nonexistence of nonzero self-orthogonal negacyclic codes over a finite field, of length relatively prime to the characteristic of the underlying field.
    Mathematics Subject Classification: Primary: 11T71; Secondary: 94B15.

    Citation:

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  • [1]

    G. K. Bakshi and M. Raka, Self-dual and self-orthogonal negacyclic codes of length $2p^n$ over a finite field, Finite Fields Appl., 19 (2013), 39-54.doi: 10.1016/j.ffa.2012.10.003.

    [2]

    T. Blackford, Negacyclic duadic codes, Finite Fields Appl., 14 (2008), 930-943.doi: 10.1016/j.ffa.2008.05.004.

    [3]

    I. F. Blake, S. Gao and R. C. Mullin, Explicit factorization of $X^{2^k}+1$ over $F_p$ with prime $p\equiv3 (mod 4)$, Appl. Algebra Engrg. Comm. Comput., 4 (1993), 89-94.doi: 10.1007/BF01386832.

    [4]

    H. Q. Dinh, Repeated-root constacyclic codes of length $2p^s$, Finite Fields Appl., 18 (2012) 133-143.doi: 10.1016/j.ffa.2011.07.003.

    [5]

    H. Q. Dinh, Structure of repeated-root constacyclic codes of length $3p^s$ and their duals, Discrete Math., 313 (2013), 983-991.doi: 10.1016/j.disc.2013.01.024.

    [6]

    W. Fu and T. Feng, On self-orthogonal group ring codes, Designs Codes Crypt., 50 (2009), 203-214.doi: 10.1007/s10623-008-9224-4.

    [7]

    W. C. Huffman, On the classification and enumeration of self-dual codes, Finite Fields Appl., 11 (2005), 451-490.doi: 10.1016/j.ffa.2005.05.012.

    [8]

    W. C. Huffman and V. Pless, Fundamentals of Error-Correcting Codes, Cambridge University Press, Cambridge, 2003.

    [9]

    Y. Jia, S. Ling and C. Xing, On self-dual cyclic codes over finite fields, IEEE Trans. Inf. Theory, 57 (2011), 2243-2251.doi: 10.1109/TIT.2010.2092415.

    [10]

    X. Kai and S. Zhu, On cyclic self-dual codes, Appl. Algebra Engrg. Comm. Comput., 19 (2008), 509-525.doi: 10.1007/s00200-008-0086-9.

    [11]

    L. Kathuria and M. Raka, Existence of cyclic self-orthogonal codes: a note on a result of Vera Pless, Adv. Math. Commun., 6 (2012), 499-503.doi: 10.3934/amc.2012.6.499.

    [12]

    R. Lidl and H. Niederreiter, Finite Fields, Cambridge University Press, Cambridge, 2008.

    [13]

    V. Pless, Cyclotomy and cyclic codes, the unreasonable effectiveness of number theory, in Proc. Sympos. Appl. Math., Amer. Math. Soc., 1992, 91-104.

    [14]

    N. J. A. Sloane and J. G. Thompson, Cyclic self-dual codes, IEEE Trans. Inf. Theory, 29 (1983), 364-367.doi: 10.1109/TIT.1983.1056682.

    [15]

    Z. Wan, Lectures on Finite Fields and Galois Rings, World Scientific Publishing, 2003.

    [16]

    W. Willems, A note on self-dual group codes, IEEE Trans. Inf. Theory, 48 (2002), 3107-3109.doi: 10.1109/TIT.2002.805076.

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