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The small weight codewords of the functional codes associated to non-singular hermitian varieties

(2010) DESIGNS CODES AND CRYPTOGRAPHY. 56(2-3). p.219-233
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Abstract
This article studies the small weight codewords of the functional code C (Herm) (X), with X a non-singular Hermitian variety of PG(N, q (2)). The main result of this article is that the small weight codewords correspond to the intersections of X with the singular Hermitian varieties of PG(N, q (2)) consisting of q + 1 hyperplanes through a common (N - 2)-dimensional space I , forming a Baer subline in the quotient space of I . The number of codewords having these small weights is also calculated. In this way, similar results are obtained to the functional codes C (2)(Q), Q a non-singular quadric (Edoukou et al., J. Pure Appl. Algebra 214:1729-1739, 2010), and C (2)(X), X a non-singular Hermitian variety (Hallez and Storme, Finite Fields Appl. 16:27-35, 2010).
Keywords
Small weight codewords, Functional codes, PROJECTIVE GEOMETRIES, Hermitian variety

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Citation

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Chicago
Edoukou, Frederic AB , Anja Hallez, Francois Rodier, and Leo Storme. 2010. “The Small Weight Codewords of the Functional Codes Associated to Non-singular Hermitian Varieties.” Designs Codes and Cryptography 56 (2-3): 219–233.
APA
Edoukou, F. A., Hallez, A., Rodier, F., & Storme, L. (2010). The small weight codewords of the functional codes associated to non-singular hermitian varieties. DESIGNS CODES AND CRYPTOGRAPHY, 56(2-3), 219–233.
Vancouver
1.
Edoukou FA, Hallez A, Rodier F, Storme L. The small weight codewords of the functional codes associated to non-singular hermitian varieties. DESIGNS CODES AND CRYPTOGRAPHY. 2010;56(2-3):219–33.
MLA
Edoukou, Frederic AB et al. “The Small Weight Codewords of the Functional Codes Associated to Non-singular Hermitian Varieties.” DESIGNS CODES AND CRYPTOGRAPHY 56.2-3 (2010): 219–233. Print.
@article{1153804,
  abstract     = {This article studies the small weight codewords of the functional code C (Herm) (X), with X a non-singular Hermitian variety of PG(N, q (2)). The main result of this article is that the small weight codewords correspond to the intersections of X with the singular Hermitian varieties of PG(N, q (2)) consisting of q + 1 hyperplanes through a common (N - 2)-dimensional space I , forming a Baer subline in the quotient space of I . The number of codewords having these small weights is also calculated. In this way, similar results are obtained to the functional codes C (2)(Q), Q a non-singular quadric (Edoukou et al., J. Pure Appl. Algebra 214:1729-1739, 2010), and C (2)(X), X a non-singular Hermitian variety (Hallez and Storme, Finite Fields Appl. 16:27-35, 2010).},
  author       = {Edoukou, Frederic AB  and Hallez, Anja and Rodier, Francois  and Storme, Leo},
  issn         = {0925-1022},
  journal      = {DESIGNS CODES AND CRYPTOGRAPHY},
  keywords     = {Small weight codewords,Functional codes,PROJECTIVE GEOMETRIES,Hermitian variety},
  language     = {eng},
  number       = {2-3},
  pages        = {219--233},
  title        = {The small weight codewords of the functional codes associated to non-singular hermitian varieties},
  url          = {http://dx.doi.org/10.1007/s10623-010-9401-0},
  volume       = {56},
  year         = {2010},
}

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