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On codes over rings invariant under affine groups

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  • We give a description of extended cyclic codes of length $p^n$ over a field and over the ring of integers modulo $p^e$ admitting the affine group $AGL_m(p^t)$, $n=mt$, as a permutation group.
    Mathematics Subject Classification: Primary: 94B15, 20B25, 94B60; Secondary: 20G40.

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  • [1]

    K. S. Abdukhalikov, Affine invariant and cyclic codes over $p$-adic numbers and finite rings, Des. Codes Cryptogr., 23 (2001), 343-370.doi: 10.1023/A:1011227228998.

    [2]

    K. S. Abdukhalikov, Codes over $p$-adic numbers and finite rings invariant under the full affine group, Finite Fields Appl., 7 (2001), 449-467.doi: 10.1006/ffta.2000.0297.

    [3]

    K. S. Abdukhalikov, Defining sets of cyclic codes invariant under the affine group, Electron. Notes Discrete Math., 6 (2001), 328-336.doi: 10.1016/S1571-0653(04)00184-2.

    [4]

    K. S. Abdukhalikov, Lattices invariant under the affine general linear group, J. Algebra, 276 (2004), 638-662.doi: 10.1016/S0021-8693(03)00496-4.

    [5]

    K. Abdukhalikov, Defining sets of extended cyclic codes invariant under the affine group, J. Pure Appl. Algebra, 196 (2005), 1-19.doi: 10.1016/j.jpaa.2004.02.016.

    [6]

    K. Abdukhalikov, E. Bannai and S. Suda, Association schemes related to universally optimal configurations, Kerdock codes and extremal Euclidean line-sets, J. Combin. Theory Ser. A, 116 (2009), 434-448.doi: 10.1016/j.jcta.2008.07.002.

    [7]

    M. Bardoe and P. Sin, The permutation modules for $GL(n+1,\mathbb F_q)$ acting on $\mathbb P^n(\mathbb F_q)$ and $\mathbb F_q^{n+1}$, J. London Math. Soc. (2), 61 (2000), 58-80.doi: 10.1112/S002461079900839X.

    [8]

    T. Berger and P. Charpin, The permutation group of affine-invariant extended cyclic codes, IEEE Trans. Inform. Theory, 42 (1996), 2194-2209.doi: 10.1109/18.556607.

    [9]

    J. T. Blackford and D. K. Ray-Chaudhuri, A transform approach to permutation groups of cyclic codes over Galois rings, IEEE Trans. Inform. Theory, 46 (2000), 2050-2058.doi: 10.1109/18.887849.

    [10]

    P. Delsarte, On cyclic codes that are invariant under the general linear group, IEEE Trans. Inform. Theory, 16 (1970), 760-769.

    [11]

    B. K. Dey and B. S. Rajan, Affine invariant extended cyclic codes over Galois rings, IEEE Trans. Inform. Theory, 50 (2004), 691-698.doi: 10.1109/TIT.2004.825044.

    [12]

    A. R. Hammons, 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. Inform. Theory, 40 (1994), 301-319.doi: 10.1109/18.312154.

    [13]

    W. C. Huffman, Codes and groups, in "Handbook of Coding Theory" (eds. V.S. Pless and W.C. Huffman), Elsevier, 2 (1998), 1345-1440.

    [14]

    T. Kasami, S. Lin and W. W. Peterson, Some results on cyclic codes which are invariant under the affine group and their applications, Inform. Control, 11 (1967), 475-496.doi: 10.1016/S0019-9958(67)90691-2.

    [15]

    P. Sin, On codes that are invariant under the affine group, Electron. J. Combin., 19 (2012), 1-14.

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