Characterization results on weighted minihypers and on linear codes meeting the Griesmer bound

Previous Article
How to say yes, no and maybe with visual cryptography
AMC Home
This Issue
Next Article
Skew constacyclic codes over Galois rings

2008, 2(3): 261-272. doi: 10.3934/amc.2008.2.261

Characterization results on weighted minihypers and on linear codes meeting the Griesmer bound

J. De Beule ^1, , K. Metsch ^2, and L. Storme ^1,

1.	Dept. of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281, S22, B-9000 Gent, Belgium, Belgium
2.	Mathematisches Institut, Universität Gieβen, Arndtstraβe 2, D-35392 Gieβen, Germany

Received January 2008 Published July 2008

Abstract
Related Papers

We present characterization results on weighted minihypers. We prove the weighted version of the original results of Hamada, Helleseth, and Maekawa. Following from the equivalence between minihypers and linear codes meeting the Griesmer bound, these characterization results are equivalent to characterization results on linear codes meeting the Griesmer bound.

Keywords: Griesmer bound, Minihypers, blocking sets..

Mathematics Subject Classification: 05B25, 51E20, 51E21, 94B0.

Citation: J. De Beule, K. Metsch, L. Storme. Characterization results on weighted minihypers and on linear codes meeting the Griesmer bound. Advances in Mathematics of Communications, 2008, 2 (3) : 261-272. doi: 10.3934/amc.2008.2.261

[1]	Ivan Landjev. On blocking sets in projective Hjelmslev planes. Advances in Mathematics of Communications, 2007, 1 (1) : 65-81. doi: 10.3934/amc.2007.1.65
[2]	Aixian Zhang, Zhengchun Zhou, Keqin Feng. A lower bound on the average Hamming correlation of frequency-hopping sequence sets. Advances in Mathematics of Communications, 2015, 9 (1) : 55-62. doi: 10.3934/amc.2015.9.55
[3]	Valentina Taddei. Bound sets for floquet boundary value problems: The nonsmooth case. Discrete & Continuous Dynamical Systems - A, 2000, 6 (2) : 459-473. doi: 10.3934/dcds.2000.6.459
[4]	Nguyen Van Thoai. Decomposition branch and bound algorithm for optimization problems over efficient sets. Journal of Industrial & Management Optimization, 2008, 4 (4) : 647-660. doi: 10.3934/jimo.2008.4.647
[5]	Xing Liu, Daiyuan Peng. Sets of frequency hopping sequences under aperiodic Hamming correlation: Upper bound and optimal constructions. Advances in Mathematics of Communications, 2014, 8 (3) : 359-373. doi: 10.3934/amc.2014.8.359
[6]	Linda Beukemann, Klaus Metsch, Leo Storme. On weighted minihypers in finite projective spaces of square order. Advances in Mathematics of Communications, 2015, 9 (3) : 291-309. doi: 10.3934/amc.2015.9.291
[7]	D. G. Aronson, N. V. Mantzaris, Hans Othmer. Wave propagation and blocking in inhomogeneous media. Discrete & Continuous Dynamical Systems - A, 2005, 13 (4) : 843-876. doi: 10.3934/dcds.2005.13.843
[8]	Fabio Camilli, Elisabetta Carlini, Claudio Marchi. A flame propagation model on a network with application to a blocking problem. Discrete & Continuous Dynamical Systems - S, 2018, 11 (5) : 825-843. doi: 10.3934/dcdss.2018051
[9]	Mikko Kaasalainen. Dynamical tomography of gravitationally bound systems. Inverse Problems & Imaging, 2008, 2 (4) : 527-546. doi: 10.3934/ipi.2008.2.527
[10]	Kazuhisa Ichikawa. Synergistic effect of blocking cancer cell invasion revealed by computer simulations. Mathematical Biosciences & Engineering, 2015, 12 (6) : 1189-1202. doi: 10.3934/mbe.2015.12.1189
[11]	Ruijun Zhao, Jemal Mohammed-Awel. A mathematical model studying mosquito-stage transmission-blocking vaccines. Mathematical Biosciences & Engineering, 2014, 11 (5) : 1229-1245. doi: 10.3934/mbe.2014.11.1229
[12]	Thomas Dauer, Marlies Gerber. Generic absence of finite blocking for interior points of Birkhoff billiards. Discrete & Continuous Dynamical Systems - A, 2016, 36 (9) : 4871-4893. doi: 10.3934/dcds.2016010
[13]	Jemal Mohammed-Awel, Ruijun Zhao, Eric Numfor, Suzanne Lenhart. Management strategies in a malaria model combining human and transmission-blocking vaccines. Discrete & Continuous Dynamical Systems - B, 2017, 22 (3) : 977-1000. doi: 10.3934/dcdsb.2017049
[14]	Demetres D. Kouvatsos, Jumma S. Alanazi, Kevin Smith. A unified ME algorithm for arbitrary open QNMs with mixed blocking mechanisms. Numerical Algebra, Control & Optimization, 2011, 1 (4) : 781-816. doi: 10.3934/naco.2011.1.781
[15]	Yang Woo Shin, Dug Hee Moon. Throughput of flow lines with unreliable parallel-machine workstations and blocking. Journal of Industrial & Management Optimization, 2017, 13 (2) : 901-916. doi: 10.3934/jimo.2016052
[16]	M. Dolfin, D. Knopoff, L. Leonida, D. Maimone Ansaldo Patti. Escaping the trap of 'blocking': A kinetic model linking economic development and political competition. Kinetic & Related Models, 2017, 10 (2) : 423-443. doi: 10.3934/krm.2017016
[17]	Marcin Dumnicki, Łucja Farnik, Halszka Tutaj-Gasińska. Asymptotic Hilbert polynomial and a bound for Waldschmidt constants. Electronic Research Announcements, 2016, 23: 8-18. doi: 10.3934/era.2016.23.002
[18]	Miklós Horváth, Márton Kiss. A bound for ratios of eigenvalues of Schrodinger operators on the real line. Conference Publications, 2005, 2005 (Special) : 403-409. doi: 10.3934/proc.2005.2005.403
[19]	John Fogarty. On Noether's bound for polynomial invariants of a finite group. Electronic Research Announcements, 2001, 7: 5-7.
[20]	Srimanta Bhattacharya, Sushmita Ruj, Bimal Roy. Combinatorial batch codes: A lower bound and optimal constructions. Advances in Mathematics of Communications, 2012, 6 (2) : 165-174. doi: 10.3934/amc.2012.6.165

2016 Impact Factor: 0.8

American Institute of Mathematical Sciences