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On the rank of incidence matrices in projective Hjelmslev spaces

(2014) DESIGNS CODES AND CRYPTOGRAPHY. 73(2). p.615-623
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Organization
Abstract
Let be a finite chain ring with , , and let . Let be an integer sequence satisfying . We consider the incidence matrix of all shape versus all shape subspaces of with . We prove that the rank of over is equal to the number of shape subspaces. This is a partial analog of Kantor's result about the rank of the incidence matrix of all dimensional versus all dimensional subspaces of . We construct an example for shapes and for which the rank of is not maximal.
Keywords
Finite chain rings, Modules over finite chain rings, Projective Hjelmslev spaces

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Citation

Please use this url to cite or link to this publication:

Chicago
Landjev, Ivan, and Peter Vandendriessche. 2014. “On the Rank of Incidence Matrices in Projective Hjelmslev Spaces.” Designs Codes and Cryptography 73 (2): 615–623.
APA
Landjev, I., & Vandendriessche, P. (2014). On the rank of incidence matrices in projective Hjelmslev spaces. DESIGNS CODES AND CRYPTOGRAPHY, 73(2), 615–623.
Vancouver
1.
Landjev I, Vandendriessche P. On the rank of incidence matrices in projective Hjelmslev spaces. DESIGNS CODES AND CRYPTOGRAPHY. 2014;73(2):615–23.
MLA
Landjev, Ivan, and Peter Vandendriessche. “On the Rank of Incidence Matrices in Projective Hjelmslev Spaces.” DESIGNS CODES AND CRYPTOGRAPHY 73.2 (2014): 615–623. Print.
@article{5722101,
  abstract     = {Let be a finite chain ring with , , and let . Let be an integer sequence satisfying . We consider the incidence matrix of all shape versus all shape subspaces of with . We prove that the rank of over is equal to the number of shape subspaces. This is a partial analog of Kantor's result about the rank of the incidence matrix of all dimensional versus all dimensional subspaces of . We construct an example for shapes and for which the rank of is not maximal.},
  author       = {Landjev, Ivan and Vandendriessche, Peter},
  issn         = {0925-1022},
  journal      = {DESIGNS CODES AND CRYPTOGRAPHY},
  keyword      = {Finite chain rings,Modules over finite chain rings,Projective Hjelmslev spaces},
  language     = {eng},
  number       = {2},
  pages        = {615--623},
  title        = {On the rank of incidence matrices in projective Hjelmslev spaces},
  volume       = {73},
  year         = {2014},
}

Web of Science
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