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The weight distributions of some irreducible cyclic codes of length $p^n$ and $2p^n$
On weighted minihypers in finite projective spaces of square order
1. | Technische Hochschule Mittelhessen, Fachbereich MND, Campus Friedberg, Wilhelm-Leuschner-Straße 13, D-61169 Friedberg, Germany |
2. | Justus-Liebig-Universität, Mathematisches Institut, Arndtstraβe 2, D-35392 Giessen, Germany |
3. | Department of Mathematics, Ghent University, Krijgslaan 281 - S22, 9000 Ghent |
References:
[1] |
A. A. Bruen, Intersection of Baer subgeometries, Arch. Math., 39 (1982), 285-288.
doi: 10.1007/BF01899537. |
[2] |
G. Donati and N. Durante, On the intersection of two subgeometries of $\PG(n, q)$, Electron. Notes Discrete Math., 26 (2006), 51-53.
doi: 10.1016/j.endm.2006.08.009. |
[3] |
S. Ferret and L. Storme, Minihypers and linear codes meeting the Griesmer bound: Improvements to results of Hamada, Helleseth and Maekawa, Des. Codes Cryptogr., 25 (2002), 143-162.
doi: 10.1023/A:1013852330818. |
[4] |
P. Govaerts and L. Storme, On a particular class of minihypers and its applications. II. Improvements for $q$ square, J. Combin. Theory Ser. A, 97 (2002), 369-393.
doi: 10.1006/jcta.2001.3219. |
[5] |
P. Govaerts and L. Storme, On a particular class of minihypers and its applications. I. The result for general $q$, Des. Codes Cryptogr., 28 (2003), 51-63.
doi: 10.1023/A:1021823703405. |
[6] |
J. H. Griesmer, A bound for error-correcting codes, IBM J. Res. Develop., 4 (1960), 532-542. |
[7] |
N. Hamada, A characterization of some $[n,k,d;q]$-codes meeting the Griesmer bound using minihypers in a finite projective geometry, Discrete Math., 116 (1993), 229-268.
doi: 10.1016/0012-365X(93)90404-H. |
[8] |
N. Hamada and T. Helleseth, A characterization of some $q$-ary codes $(q>(h-1)^2, h\geq 3)$ meeting the Griesmer bound, Math. Japonica, 38 (1993), 925-940. |
[9] |
N. Hamada and T. Helleseth, Codes and minihypers, in Optimal Codes and Related Topics, Bulgaria, 2001, 79-84. |
[10] |
G. Solomon and J. J. Stiffler, Algebraically punctured cyclic codes, Inform. Control, 8 (1965), 170-179. |
[11] |
L. Storme, Weighted ${\delta(q+1),\delta;k-1,q}$-minihypers, Discrete Math., 308 (2008), 339-354.
doi: 10.1016/j.disc.2006.11.048. |
[12] |
M. Sved, Baer subspaces in the $n$-dimensional projective space, in Combinatorial Mathematics X, Springer, 1983, 375-391.
doi: 10.1007/BFb0071531. |
show all references
References:
[1] |
A. A. Bruen, Intersection of Baer subgeometries, Arch. Math., 39 (1982), 285-288.
doi: 10.1007/BF01899537. |
[2] |
G. Donati and N. Durante, On the intersection of two subgeometries of $\PG(n, q)$, Electron. Notes Discrete Math., 26 (2006), 51-53.
doi: 10.1016/j.endm.2006.08.009. |
[3] |
S. Ferret and L. Storme, Minihypers and linear codes meeting the Griesmer bound: Improvements to results of Hamada, Helleseth and Maekawa, Des. Codes Cryptogr., 25 (2002), 143-162.
doi: 10.1023/A:1013852330818. |
[4] |
P. Govaerts and L. Storme, On a particular class of minihypers and its applications. II. Improvements for $q$ square, J. Combin. Theory Ser. A, 97 (2002), 369-393.
doi: 10.1006/jcta.2001.3219. |
[5] |
P. Govaerts and L. Storme, On a particular class of minihypers and its applications. I. The result for general $q$, Des. Codes Cryptogr., 28 (2003), 51-63.
doi: 10.1023/A:1021823703405. |
[6] |
J. H. Griesmer, A bound for error-correcting codes, IBM J. Res. Develop., 4 (1960), 532-542. |
[7] |
N. Hamada, A characterization of some $[n,k,d;q]$-codes meeting the Griesmer bound using minihypers in a finite projective geometry, Discrete Math., 116 (1993), 229-268.
doi: 10.1016/0012-365X(93)90404-H. |
[8] |
N. Hamada and T. Helleseth, A characterization of some $q$-ary codes $(q>(h-1)^2, h\geq 3)$ meeting the Griesmer bound, Math. Japonica, 38 (1993), 925-940. |
[9] |
N. Hamada and T. Helleseth, Codes and minihypers, in Optimal Codes and Related Topics, Bulgaria, 2001, 79-84. |
[10] |
G. Solomon and J. J. Stiffler, Algebraically punctured cyclic codes, Inform. Control, 8 (1965), 170-179. |
[11] |
L. Storme, Weighted ${\delta(q+1),\delta;k-1,q}$-minihypers, Discrete Math., 308 (2008), 339-354.
doi: 10.1016/j.disc.2006.11.048. |
[12] |
M. Sved, Baer subspaces in the $n$-dimensional projective space, in Combinatorial Mathematics X, Springer, 1983, 375-391.
doi: 10.1007/BFb0071531. |
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