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There is no $[24,12,9]$ doubly-even self-dual code over $\mathbb F_4$
Explicit constructions of some non-Gabidulin linear maximum rank distance codes
1. | Department of Mathematics & Institute of Applied Mathematics, Middle East Technical University, 06800, Ankara, Turkey |
2. | Department of Mathematics and Institute of Applied Mathematics, Middle East Technical University, Dumlupnar Bulvar, 06800, Ankara |
References:
[1] |
J. Berson, Linearized polynomial maps over finite fields,, J. Algebra, 399 (2014), 389.
doi: 10.1016/j.jalgebra.2013.10.013. |
[2] |
J. de la Cruz, M. Kiermaier, A. Wassermann and W. Willems, Algebraic structures of MRD Codes,, Adv. Math. Commun., 10 (2016), 499.
doi: 10.3934/amc.2016021. |
[3] |
P. Delsarte, Bilinear forms over a finite field, with applications to coding theory,, J. Comb. Theory A, 25 (1978), 226.
doi: 10.1016/0097-3165(78)90015-8. |
[4] |
E. M. Gabidulin, Theory of codes with maximum rank distance,, Probl. Inform. Transm., 21 (1985), 1.
|
[5] |
A.-L. Horlemann-Trautmann and K. Marshall, New criteria for MRD and Gabidulin codes and some rank-metric code constructions,, preprint, (). Google Scholar |
[6] |
A. Kshevetskiy and E. Gabidulin, The new construction of rank codes,, in Proc. Int. Symp. Inf. Theory (ISIT 2005), (2005), 2105. Google Scholar |
[7] |
R. Lidl and H. Niederreiter, Finite Fields,, Cambridge Univ. Press, (1997).
|
[8] |
K. Morrison, Equivalence of rank-metric and matrix codes and automorphism groups of Gabidulin codes,, IEEE Trans. Inf. Theory, 60 (2014), 7035.
doi: 10.1109/TIT.2014.2359198. |
[9] |
O. Ore, On a special class of polynomials,, Trans. Amer. Math. Soc., 35 (1933), 559.
doi: 10.2307/1989849. |
[10] |
J. Sheekey, A new family of linear maximum rank distance codes,, preprint, (). Google Scholar |
show all references
References:
[1] |
J. Berson, Linearized polynomial maps over finite fields,, J. Algebra, 399 (2014), 389.
doi: 10.1016/j.jalgebra.2013.10.013. |
[2] |
J. de la Cruz, M. Kiermaier, A. Wassermann and W. Willems, Algebraic structures of MRD Codes,, Adv. Math. Commun., 10 (2016), 499.
doi: 10.3934/amc.2016021. |
[3] |
P. Delsarte, Bilinear forms over a finite field, with applications to coding theory,, J. Comb. Theory A, 25 (1978), 226.
doi: 10.1016/0097-3165(78)90015-8. |
[4] |
E. M. Gabidulin, Theory of codes with maximum rank distance,, Probl. Inform. Transm., 21 (1985), 1.
|
[5] |
A.-L. Horlemann-Trautmann and K. Marshall, New criteria for MRD and Gabidulin codes and some rank-metric code constructions,, preprint, (). Google Scholar |
[6] |
A. Kshevetskiy and E. Gabidulin, The new construction of rank codes,, in Proc. Int. Symp. Inf. Theory (ISIT 2005), (2005), 2105. Google Scholar |
[7] |
R. Lidl and H. Niederreiter, Finite Fields,, Cambridge Univ. Press, (1997).
|
[8] |
K. Morrison, Equivalence of rank-metric and matrix codes and automorphism groups of Gabidulin codes,, IEEE Trans. Inf. Theory, 60 (2014), 7035.
doi: 10.1109/TIT.2014.2359198. |
[9] |
O. Ore, On a special class of polynomials,, Trans. Amer. Math. Soc., 35 (1933), 559.
doi: 10.2307/1989849. |
[10] |
J. Sheekey, A new family of linear maximum rank distance codes,, preprint, (). Google Scholar |
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