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The geometric structure of relative one-weight codes
Codes over local rings of order 16 and binary codes
1. | Department of Mathematics, University of Scranton, Scranton, PA 18510, United States, United States |
2. | Department of Mathematics and Statistics, Eastern Kentucky University Richmond, KY 40475, United States |
References:
[1] |
J. H. Conway and N. J. A. Sloane, A new upper bound on the minimal distance of self-dual codes, IEEE-IT, 36 (1990), 1319-1333.
doi: 10.1109/18.59931. |
[2] |
S. T. Dougherty and C. Fernandez-Cordoba, Codes over $\mathbbZ_{2^k}$, Gray maps and self-dual codes, Adv. Math. Commun., 5 (2011), 571-588.
doi: 10.3934/amc.2011.5.571. |
[3] |
S. T. Dougherty, P. Gaborit, M. Harada, A. Munemasa and P. Solé, Type IV self-dual codes over rings, IEEE-IT, 45 (1999), 2345-2360.
doi: 10.1109/18.796375. |
[4] |
S. T. Dougherty, J. L. Kim, H. Kulosman and H. Liu, Self-dual codes over Frobenius rings, Finite Fields Appl., 16 (2010), 14-26.
doi: 10.1016/j.ffa.2009.11.004. |
[5] |
S. T. Dougherty and H. Liu, Independence of vectors in codes over rings, Des. Codes Crypt., 51 (2009), 55-68.
doi: 10.1007/s10623-008-9243-1. |
[6] |
S. T. Dougherty and K. Shiromoto, Maximum distance codes over rings of order 4, IEEE-IT, 47 (2001), 400-404.
doi: 10.1109/18.904544. |
[7] |
S. T. Dougherty, B. Yildiz and S. Karadeniz, Codes over $R_k$, Gray maps and their binary images, Finite Fields Appl., 17 (2011), 205-219.
doi: 10.1016/j.ffa.2010.11.002. |
[8] |
A. R. Hammons Jr., 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-IT, 40 (1994), 301-319.
doi: 10.1109/18.312154. |
[9] |
F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam, 1977. |
[10] |
E. Martinez-Moro and S. Szabo, On codes over local Frobenius non-chain rings of order 16, Contemp. Math., 634 (2015), 227-242
doi: 10.1090/conm/634/12702. |
[11] |
J. Wood, Duality for modules over finite rings and applications to coding theory, Amer. J. Math., 121 (1999), 555-575. |
[12] |
B. Yildiz and S. Karadeniz, Linear codes over $\mathbbF_2 + u \mathbbF_2 + v \mathbbF_2 + uv \mathbbF_2$, Des. Codes Crypt., 54 (2010), 61-81.
doi: 10.1007/s10623-009-9309-8. |
[13] |
B. Yildiz and S. Karadeniz, A new construction for the extended binary Golay code, Appl. Math. Inf. Sci., 8 (2014), 69-72.
doi: 10.12785/amis/080107. |
[14] |
B. Yildiz and S. Karadeniz, Linear codes over $\mathbbZ_4 + u \mathbbZ_4$, MacWilliams identities, projections, and formally self-dual codes, Finite Fields Appl., 27 (2014), 24-40.
doi: 10.1016/j.ffa.2013.12.007. |
show all references
References:
[1] |
J. H. Conway and N. J. A. Sloane, A new upper bound on the minimal distance of self-dual codes, IEEE-IT, 36 (1990), 1319-1333.
doi: 10.1109/18.59931. |
[2] |
S. T. Dougherty and C. Fernandez-Cordoba, Codes over $\mathbbZ_{2^k}$, Gray maps and self-dual codes, Adv. Math. Commun., 5 (2011), 571-588.
doi: 10.3934/amc.2011.5.571. |
[3] |
S. T. Dougherty, P. Gaborit, M. Harada, A. Munemasa and P. Solé, Type IV self-dual codes over rings, IEEE-IT, 45 (1999), 2345-2360.
doi: 10.1109/18.796375. |
[4] |
S. T. Dougherty, J. L. Kim, H. Kulosman and H. Liu, Self-dual codes over Frobenius rings, Finite Fields Appl., 16 (2010), 14-26.
doi: 10.1016/j.ffa.2009.11.004. |
[5] |
S. T. Dougherty and H. Liu, Independence of vectors in codes over rings, Des. Codes Crypt., 51 (2009), 55-68.
doi: 10.1007/s10623-008-9243-1. |
[6] |
S. T. Dougherty and K. Shiromoto, Maximum distance codes over rings of order 4, IEEE-IT, 47 (2001), 400-404.
doi: 10.1109/18.904544. |
[7] |
S. T. Dougherty, B. Yildiz and S. Karadeniz, Codes over $R_k$, Gray maps and their binary images, Finite Fields Appl., 17 (2011), 205-219.
doi: 10.1016/j.ffa.2010.11.002. |
[8] |
A. R. Hammons Jr., 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-IT, 40 (1994), 301-319.
doi: 10.1109/18.312154. |
[9] |
F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam, 1977. |
[10] |
E. Martinez-Moro and S. Szabo, On codes over local Frobenius non-chain rings of order 16, Contemp. Math., 634 (2015), 227-242
doi: 10.1090/conm/634/12702. |
[11] |
J. Wood, Duality for modules over finite rings and applications to coding theory, Amer. J. Math., 121 (1999), 555-575. |
[12] |
B. Yildiz and S. Karadeniz, Linear codes over $\mathbbF_2 + u \mathbbF_2 + v \mathbbF_2 + uv \mathbbF_2$, Des. Codes Crypt., 54 (2010), 61-81.
doi: 10.1007/s10623-009-9309-8. |
[13] |
B. Yildiz and S. Karadeniz, A new construction for the extended binary Golay code, Appl. Math. Inf. Sci., 8 (2014), 69-72.
doi: 10.12785/amis/080107. |
[14] |
B. Yildiz and S. Karadeniz, Linear codes over $\mathbbZ_4 + u \mathbbZ_4$, MacWilliams identities, projections, and formally self-dual codes, Finite Fields Appl., 27 (2014), 24-40.
doi: 10.1016/j.ffa.2013.12.007. |
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