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Galois geometries and coding theory

Tuvi Etzion and Leo Storme (UGent)
(2016) DESIGNS CODES AND CRYPTOGRAPHY. 78(1). p.311-350
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Abstract
Galois geometries and coding theory are two research areas which have been interacting with each other for many decades. From the early examples linking linear MDS codes with arcs in finite projective spaces, linear codes meeting the Griesmer bound with minihypers, covering radius with saturating sets, links have evolved to functional codes, generalized projective Reed-Muller codes, and even further to LDPC codes, random network codes, and distributed storage. This article reviews briefly the known links, and then focuses on new links and new directions. We present new results and open problems to stimulate the research on Galois geometries, coding theory, and on their continuously developing and increasing interactions.
Keywords
REED-MULLER CODES, FUNCTIONAL CODES, SMALL BLOCKING SETS, CONSTANT DIMENSION CODES, ERROR-CORRECTING CODES, FINITE PROJECTIVE SPACES, Designs and codes over vector spaces, Network coding, Galois geometries, Coding theory, T-DESIGNS, HERMITIAN VARIETIES, VECTOR-SPACES, Q-ANALOGS

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Chicago
Etzion, Tuvi, and Leo Storme. 2016. “Galois Geometries and Coding Theory.” Ed. Dieter Jungnickel, Jennifer Key, Chris Mitchell, Ronald Mullin, and Peter Wild. Designs Codes and Cryptography 78 (1): 311–350.
APA
Etzion, T., & Storme, L. (2016). Galois geometries and coding theory. (D. Jungnickel, J. Key, C. Mitchell, R. Mullin, & P. Wild, Eds.)DESIGNS CODES AND CRYPTOGRAPHY, 78(1), 311–350.
Vancouver
1.
Etzion T, Storme L. Galois geometries and coding theory. Jungnickel D, Key J, Mitchell C, Mullin R, Wild P, editors. DESIGNS CODES AND CRYPTOGRAPHY. 2016;78(1):311–50.
MLA
Etzion, Tuvi, and Leo Storme. “Galois Geometries and Coding Theory.” Ed. Dieter Jungnickel et al. DESIGNS CODES AND CRYPTOGRAPHY 78.1 (2016): 311–350. Print.
@article{8028399,
  abstract     = {Galois geometries and coding theory are two research areas which have been interacting with each other for many decades. From the early examples linking linear MDS codes with arcs in finite projective spaces, linear codes meeting the Griesmer bound with minihypers, covering radius with saturating sets, links have evolved to functional codes, generalized projective Reed-Muller codes, and even further to LDPC codes, random network codes, and distributed storage. This article reviews briefly the known links, and then focuses on new links and new directions. We present new results and open problems to stimulate the research on Galois geometries, coding theory, and on their continuously developing and increasing interactions.},
  author       = {Etzion, Tuvi and Storme, Leo},
  editor       = {Jungnickel, Dieter and Key, Jennifer and Mitchell, Chris and Mullin, Ronald and Wild, Peter},
  issn         = {0925-1022},
  journal      = {DESIGNS CODES AND CRYPTOGRAPHY},
  keywords     = {REED-MULLER CODES,FUNCTIONAL CODES,SMALL BLOCKING SETS,CONSTANT DIMENSION CODES,ERROR-CORRECTING CODES,FINITE PROJECTIVE SPACES,Designs and codes over vector spaces,Network coding,Galois geometries,Coding theory,T-DESIGNS,HERMITIAN VARIETIES,VECTOR-SPACES,Q-ANALOGS},
  language     = {eng},
  number       = {1},
  pages        = {311--350},
  title        = {Galois geometries and coding theory},
  url          = {http://dx.doi.org/10.1007/s10623-015-0156-5},
  volume       = {78},
  year         = {2016},
}

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