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On the duality and the direction of polycyclic codes

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  • Polycyclic codes are ideals in quotients of polynomial rings by a principal ideal. Special cases are cyclic and constacyclic codes. A MacWilliams relation between such a code and its annihilator ideal is derived. An infinite family of binary self-dual codes that are also formally self-dual in the classical sense is exhibited. We show that right polycyclic codes are left polycyclic codes with different (explicit) associate vectors and characterize the case when a code is both left and right polycyclic for the same associate polynomial. A similar study is led for sequential codes.
    Mathematics Subject Classification: Primary: 94B15, 94B05, 94B065.


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  • [1]

    K. Betsumiya and M. Harada, Binary optimal odd formally self-dual codes, Des. Codes Crypt., 23 (2001), 11-22.doi: 10.1023/A:1011203416769.


    J. Fields, P. Gaborit, V. Pless and W. C. Huffman, On the classification of extremal even formally self-dual codes of lengths $20$ and $22$, Discrete Appl. Math., 111 (2001), 75-86.doi: 10.1016/S0166-218X(00)00345-0.


    M. Grassl, Bounds on the minimum distance of linear codes, available online at http://www.codetables.de


    W. C. Huffman and V. Pless, Fundamentals of Error Correcting Codes, Cambridge Univ. Press, 2003.doi: 10.1017/CBO9780511807077.


    T. Kasami, Optimum shortened cyclic codes for burst-error correction, IEEE Trans. Inform. Theory, 9 (1963), 105-109.


    J.-L. Kim and V. Pless, A note on formally self-dual even codes of length divisible by 8, Finite Fields Appl., 13 (2007), 224-229.doi: 10.1016/j.ffa.2005.09.006.


    S. R. Lopez-Permouth, B. R. Parra-Avila and S. Szabo, Dual generalizations of the concept of cyclicity of codes, Adv. Math. Commun., 3 (2009), 227-234.doi: 10.3934/amc.2009.3.227.


    F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam, 1977.


    M. Matsuoka, $\theta$-polycyclic codes and $\theta$-sequential codes over finite fields, Int. J. Algebra, 5 (2011), 65-70.


    W. W. Peterson and E. J. Weldon, Error Correcting Codes, MIT Press, 1972.


    E. M. Rains and N. J. A. Sloane, Self-dual codes, in Handbook of Coding Theory, Elsevier, Amsterdam, 1998.


    J. Wood, Duality for modules over finite rings and applications to coding theory, Amer. J. Math., 121 (1999), 555-575.

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