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Linear codes from projective spaces

Michel Lavrauw (UGent), Leo Storme (UGent) and Geertrui Van de Voorde (UGent)
(2010) Contemporary Mathematics. 523. p.185-202
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Abstract
The linear code C-s,C- (t)(n,q) of s-spaces and t-spaces in a projective space PG(n,q), q = p(h), p prime, is defined as the vector space spanned over F-p by the rows of the incidence matrix of s-spaces and t-spaces. This code generalises the code of points and lines in a projective plane, which has been intensively studied since the 1970's. In this paper, we give an overview of what is currently known about the codes C-s,C-t(n,q) and their duals.
Keywords
Projective planes, Projective spaces, Blocking sets, Unitals, Linear codes, SMALL WEIGHT CODEWORDS, INCIDENCE MATRIX, GEOMETRIC CODES, MINIMUM WEIGHT, CYCLIC CODES, DUAL CODES, K-SPACES, PLANES, ORDER-9, POINTS

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Chicago
Lavrauw, Michel, Leo Storme, and Geertrui Van de Voorde. 2010. “Linear Codes from Projective Spaces.” In Contemporary Mathematics, ed. AA Bruen and DL Wehlau, 523:185–202. Providence, RI, USA: American Mathematical Society (AMS).
APA
Lavrauw, M., Storme, L., & Van de Voorde, G. (2010). Linear codes from projective spaces. In A. Bruen & D. Wehlau (Eds.), Contemporary Mathematics (Vol. 523, pp. 185–202). Presented at the Conference on Error-Control Codes, Information Theory and Applied Cryptography, Providence, RI, USA: American Mathematical Society (AMS).
Vancouver
1.
Lavrauw M, Storme L, Van de Voorde G. Linear codes from projective spaces. In: Bruen A, Wehlau D, editors. Contemporary Mathematics. Providence, RI, USA: American Mathematical Society (AMS); 2010. p. 185–202.
MLA
Lavrauw, Michel, Leo Storme, and Geertrui Van de Voorde. “Linear Codes from Projective Spaces.” Contemporary Mathematics. Ed. AA Bruen & DL Wehlau. Vol. 523. Providence, RI, USA: American Mathematical Society (AMS), 2010. 185–202. Print.
@inproceedings{1261269,
  abstract     = {The linear code C-s,C- (t)(n,q) of s-spaces and t-spaces in a projective space PG(n,q), q = p(h), p prime, is defined as the vector space spanned over F-p by the rows of the incidence matrix of s-spaces and t-spaces. This code generalises the code of points and lines in a projective plane, which has been intensively studied since the 1970's. In this paper, we give an overview of what is currently known about the codes C-s,C-t(n,q) and their duals.},
  author       = {Lavrauw, Michel and Storme, Leo and Van de Voorde, Geertrui},
  booktitle    = {Contemporary Mathematics},
  editor       = {Bruen, AA and Wehlau, DL},
  isbn         = {9780821849569},
  issn         = {0271-4132},
  keyword      = {Projective planes,Projective spaces,Blocking sets,Unitals,Linear codes,SMALL WEIGHT CODEWORDS,INCIDENCE MATRIX,GEOMETRIC CODES,MINIMUM WEIGHT,CYCLIC CODES,DUAL CODES,K-SPACES,PLANES,ORDER-9,POINTS},
  language     = {eng},
  location     = {Toronto, ON, Canada},
  pages        = {185--202},
  publisher    = {American Mathematical Society (AMS)},
  title        = {Linear codes from projective spaces},
  volume       = {523},
  year         = {2010},
}

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