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Explicit constructions of some non-Gabidulin linear maximum rank distance codes
The non-existence of $(104,22;3,5)$-arcs
1. | Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev str. bl. 8, Sofia 1113 |
2. | Faculty of Mathematics and Informatics, Sofia University, 5, James Bourchier blvd., 1164 Sofia, Bulgaria |
References:
[1] |
S. Ball, On intersection sets in Desarguesian affine spaces, European J. Combin., 21 (2000), 441-446.
doi: 10.1006/eujc.2000.0350. |
[2] |
I. Boukliev, Optimal Linear Codes - Constructions and Bounds, Ph.D thesis, Sofia, 1996. |
[3] |
S. Dodunekov and J. Simonis, Codes and projective multisets, Electr. J. Combin., 5 (1998), #R37. |
[4] |
Y. Edel and I. Landjev, On multiple caps in finite projective spaces, Des. Codes Cryptogr., 56 (2010), 163-175.
doi: 10.1007/s10623-010-9398-4. |
[5] |
J. H. Griesmer, A bound for error-correcting codes, IBM J. Res. Develop., 4 (1960), 532-542. |
[6] |
R. Hill, Optimal linear codes, in Cryptography and Coding (ed. C. Mitchell), Oxford Univ. Press, 1992, 75-104. |
[7] |
R. Hill and E. Kolev, A survey of recent results on optimal linear codes, in Combinatorial Designs and their Application (eds. F.C. Holroyd, K.A.S. Quinn, Ch. Rowley and B.S. Webb), Chapman & Hall CRC, 1999, 127-152. |
[8] |
I. Landjev, The geometry of $(n,3)$-arcs in the projective plane of order 5, in Proc. 6th Workshop ACCT, Sozopol, 1996, 170-175. |
[9] |
I. Landjev and A. Rousseva, On the Extendability of Griesmer Arcs, Ann. Sof. Univ. Fac. Math. Inf., 101 (2013), 183-192. |
[10] |
I. Landjev, A. Rousseva and L. Storme, On the extendability of quasidivisible Griesmer arcs, Des. Codes Cryptogr., 79 (2016), 535-547.
doi: 10.1007/s10623-015-0114-2. |
[11] |
I. Landjev and L. Storme, Linear codes and Galois geometries, in Current Research Topics in Galois Geometries (eds. L. Storme and J. De Beule), NOVA Publishers, 2012, 187-214. |
[12] |
T. Maruta, A new extension theorem for linear codes, Finite Fields Appl., 10 (2004), 674-685.
doi: 10.1016/j.ffa.2004.02.001. |
[13] |
T. Maruta, http://www.mi.s.oskafu-u.ac.jp/~maruta/griesmer.htm |
[14] |
A. Rousseva, On the structure of $(t$ mod $q)$-arcs in finite projective geometries, Annuaire de l' Univ. de Sofia, 102 (2015), to appear. |
[15] |
G. Solomon and J. J. Stiffler, Algebraically punctured cyclic codes, Inform. Control, 8 (1965) 170-179. |
show all references
References:
[1] |
S. Ball, On intersection sets in Desarguesian affine spaces, European J. Combin., 21 (2000), 441-446.
doi: 10.1006/eujc.2000.0350. |
[2] |
I. Boukliev, Optimal Linear Codes - Constructions and Bounds, Ph.D thesis, Sofia, 1996. |
[3] |
S. Dodunekov and J. Simonis, Codes and projective multisets, Electr. J. Combin., 5 (1998), #R37. |
[4] |
Y. Edel and I. Landjev, On multiple caps in finite projective spaces, Des. Codes Cryptogr., 56 (2010), 163-175.
doi: 10.1007/s10623-010-9398-4. |
[5] |
J. H. Griesmer, A bound for error-correcting codes, IBM J. Res. Develop., 4 (1960), 532-542. |
[6] |
R. Hill, Optimal linear codes, in Cryptography and Coding (ed. C. Mitchell), Oxford Univ. Press, 1992, 75-104. |
[7] |
R. Hill and E. Kolev, A survey of recent results on optimal linear codes, in Combinatorial Designs and their Application (eds. F.C. Holroyd, K.A.S. Quinn, Ch. Rowley and B.S. Webb), Chapman & Hall CRC, 1999, 127-152. |
[8] |
I. Landjev, The geometry of $(n,3)$-arcs in the projective plane of order 5, in Proc. 6th Workshop ACCT, Sozopol, 1996, 170-175. |
[9] |
I. Landjev and A. Rousseva, On the Extendability of Griesmer Arcs, Ann. Sof. Univ. Fac. Math. Inf., 101 (2013), 183-192. |
[10] |
I. Landjev, A. Rousseva and L. Storme, On the extendability of quasidivisible Griesmer arcs, Des. Codes Cryptogr., 79 (2016), 535-547.
doi: 10.1007/s10623-015-0114-2. |
[11] |
I. Landjev and L. Storme, Linear codes and Galois geometries, in Current Research Topics in Galois Geometries (eds. L. Storme and J. De Beule), NOVA Publishers, 2012, 187-214. |
[12] |
T. Maruta, A new extension theorem for linear codes, Finite Fields Appl., 10 (2004), 674-685.
doi: 10.1016/j.ffa.2004.02.001. |
[13] |
T. Maruta, http://www.mi.s.oskafu-u.ac.jp/~maruta/griesmer.htm |
[14] |
A. Rousseva, On the structure of $(t$ mod $q)$-arcs in finite projective geometries, Annuaire de l' Univ. de Sofia, 102 (2015), to appear. |
[15] |
G. Solomon and J. J. Stiffler, Algebraically punctured cyclic codes, Inform. Control, 8 (1965) 170-179. |
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