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Further results on the classification of MDS codes
1. | Department of Communications and Networking, School of Electrical Engineering, Aalto University, P.O. Box 13000, 00076 Aalto, Finland |
References:
[1] |
T. L. Alderson, $(6,3)$-MDS codes over an alphabet of size 4, Des. Codes Cryptogr., 38 (2006), 31-40.
doi: 10.1007/s10623-004-5659-4. |
[2] |
T. L. Alderson, A. A. Bruen and R. Silverman, Maximum distance separable codes and arcs in projective spaces, J. Combin. Theory Ser. A, 114 (2007), 1101-1117.
doi: 10.1016/j.jcta.2006.11.005. |
[3] |
T. L. Alderson and A. Gács, On the maximality of linear codes, Des. Codes Cryptogr., 53 (2009), 59-68.
doi: 10.1007/s10623-009-9293-z. |
[4] |
S. Ball, On sets of vectors of a finite vector space in which every subset of basis size is a basis, J. Eur. Math. Soc., 14 (2012), 733-748.
doi: 10.4171/JEMS/316. |
[5] |
S. Ball and J. De Beule, On sets of vectors of a finite vector space in which every subset of basis size is a basis II, Des. Codes Cryptogr., 65 (2012), 5-14.
doi: 10.1007/s10623-012-9658-6. |
[6] |
A. Betten, M. Braun, H. Fripertinger, A. Kerber, A. Kohnert and A. Wassermann, Error-Correcting Linear Codes: Classification by Isometry and Applications, Springer, Berlin, 2006. |
[7] |
J. Egan and I. M. Wanless, Enumeration of MOLS of small order, Math. Comp., 85 (2016), 799-824.
doi: 10.1090/mcom/3010. |
[8] |
P. Kaski and P. R. J. Östergård, Classification Algorithms for Codes and Designs, Springer, Berlin, 2006. |
[9] |
P. Kaski and O. Pottonen, Libexact User's Guide, version 1.0, Technical Reports TR 2008-1, Helsinki Inst. Inform. Techn., Helsinki, 2008. |
[10] |
G. Kéri, Types of superregular matrices and the number of $n$-arcs and complete $n$-arcs in $PG(r, q)$, J. Combin. Des., 14 (2006), 363-390.
doi: 10.1002/jcd.20091. |
[11] |
J. I. Kokkala, D. S. Krotov and P. R. J. Östergård, On the classification of MDS codes, IEEE Trans. Inf. Theory, 61 (2015), 6485-6492.
doi: 10.1109/TIT.2015.2488659. |
[12] |
J. I. Kokkala and P. R. J. Östergård, Classification of Graeco-Latin cubes, J. Combin. Des., 23 (2015), 509-512.
doi: 10.1002/jcd.21400. |
[13] |
F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam, 1977. |
[14] |
B. M. Maenhaut and I. M. Wanless, Atomic Latin squares of order eleven, J. Combin. Des., 12 (2004), 12-34.
doi: 10.1002/jcd.10064. |
[15] |
B. D. McKay, A. Meynert and W. Myrvold, Small Latin squares, quasigroups, and loops, J. Combin. Des., 15 (2007), 98-119.
doi: 10.1002/jcd.20105. |
[16] |
B. D. McKay and A. Piperno, Practical graph isomorphism, II, J. Symbolic Comput., 60 (2014), 94-112.
doi: 10.1016/j.jsc.2013.09.003. |
[17] |
B. D. McKay and I. M. Wanless, A census of small Latin hypercubes, SIAM J. Discrete Math., 22 (2008), 719-736.
doi: 10.1137/070693874. |
[18] |
S. Niskanen and P. R. J. Östergård, Cliquer User's guide, Version 1.0, Technical Report T48, Communications Laboratory, Helsinki Univ. Techn., Espoo, 2003. |
[19] |
P. R. J. Östergård, Constructing combinatorial objects via cliques, in Surveys in Combinatorics 2005 (ed. B. S. Webb), Cambridge Univ. Press, Cambridge, 2005, 57-82.
doi: 10.1017/CBO9780511734885.004. |
[20] |
E. T. Parker, Computer investigation of orthogonal Latin squares of order ten, in Proc. Sympos. Appl. Math., Amer. Math. Soc., Providence, 1963, 73-81. |
[21] |
V. N. Potapov and D. S. Krotov, On the number of $n$-ary quasigroups of finite order, Discrete Math. Appl., 21 (2011), 575-585.
doi: 10.1016/j.disc.2010.09.023. |
[22] |
B. Segre, Curve razionali normali e $k$-archi negli spazi finiti, Ann. Mat. Pura Appl., 39 (1955), 357-379.
doi: 10.1007/BF02410779. |
show all references
References:
[1] |
T. L. Alderson, $(6,3)$-MDS codes over an alphabet of size 4, Des. Codes Cryptogr., 38 (2006), 31-40.
doi: 10.1007/s10623-004-5659-4. |
[2] |
T. L. Alderson, A. A. Bruen and R. Silverman, Maximum distance separable codes and arcs in projective spaces, J. Combin. Theory Ser. A, 114 (2007), 1101-1117.
doi: 10.1016/j.jcta.2006.11.005. |
[3] |
T. L. Alderson and A. Gács, On the maximality of linear codes, Des. Codes Cryptogr., 53 (2009), 59-68.
doi: 10.1007/s10623-009-9293-z. |
[4] |
S. Ball, On sets of vectors of a finite vector space in which every subset of basis size is a basis, J. Eur. Math. Soc., 14 (2012), 733-748.
doi: 10.4171/JEMS/316. |
[5] |
S. Ball and J. De Beule, On sets of vectors of a finite vector space in which every subset of basis size is a basis II, Des. Codes Cryptogr., 65 (2012), 5-14.
doi: 10.1007/s10623-012-9658-6. |
[6] |
A. Betten, M. Braun, H. Fripertinger, A. Kerber, A. Kohnert and A. Wassermann, Error-Correcting Linear Codes: Classification by Isometry and Applications, Springer, Berlin, 2006. |
[7] |
J. Egan and I. M. Wanless, Enumeration of MOLS of small order, Math. Comp., 85 (2016), 799-824.
doi: 10.1090/mcom/3010. |
[8] |
P. Kaski and P. R. J. Östergård, Classification Algorithms for Codes and Designs, Springer, Berlin, 2006. |
[9] |
P. Kaski and O. Pottonen, Libexact User's Guide, version 1.0, Technical Reports TR 2008-1, Helsinki Inst. Inform. Techn., Helsinki, 2008. |
[10] |
G. Kéri, Types of superregular matrices and the number of $n$-arcs and complete $n$-arcs in $PG(r, q)$, J. Combin. Des., 14 (2006), 363-390.
doi: 10.1002/jcd.20091. |
[11] |
J. I. Kokkala, D. S. Krotov and P. R. J. Östergård, On the classification of MDS codes, IEEE Trans. Inf. Theory, 61 (2015), 6485-6492.
doi: 10.1109/TIT.2015.2488659. |
[12] |
J. I. Kokkala and P. R. J. Östergård, Classification of Graeco-Latin cubes, J. Combin. Des., 23 (2015), 509-512.
doi: 10.1002/jcd.21400. |
[13] |
F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam, 1977. |
[14] |
B. M. Maenhaut and I. M. Wanless, Atomic Latin squares of order eleven, J. Combin. Des., 12 (2004), 12-34.
doi: 10.1002/jcd.10064. |
[15] |
B. D. McKay, A. Meynert and W. Myrvold, Small Latin squares, quasigroups, and loops, J. Combin. Des., 15 (2007), 98-119.
doi: 10.1002/jcd.20105. |
[16] |
B. D. McKay and A. Piperno, Practical graph isomorphism, II, J. Symbolic Comput., 60 (2014), 94-112.
doi: 10.1016/j.jsc.2013.09.003. |
[17] |
B. D. McKay and I. M. Wanless, A census of small Latin hypercubes, SIAM J. Discrete Math., 22 (2008), 719-736.
doi: 10.1137/070693874. |
[18] |
S. Niskanen and P. R. J. Östergård, Cliquer User's guide, Version 1.0, Technical Report T48, Communications Laboratory, Helsinki Univ. Techn., Espoo, 2003. |
[19] |
P. R. J. Östergård, Constructing combinatorial objects via cliques, in Surveys in Combinatorics 2005 (ed. B. S. Webb), Cambridge Univ. Press, Cambridge, 2005, 57-82.
doi: 10.1017/CBO9780511734885.004. |
[20] |
E. T. Parker, Computer investigation of orthogonal Latin squares of order ten, in Proc. Sympos. Appl. Math., Amer. Math. Soc., Providence, 1963, 73-81. |
[21] |
V. N. Potapov and D. S. Krotov, On the number of $n$-ary quasigroups of finite order, Discrete Math. Appl., 21 (2011), 575-585.
doi: 10.1016/j.disc.2010.09.023. |
[22] |
B. Segre, Curve razionali normali e $k$-archi negli spazi finiti, Ann. Mat. Pura Appl., 39 (1955), 357-379.
doi: 10.1007/BF02410779. |
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