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On the functional codes defined by quadrics and Hermitian varieties

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Abstract
In recent years, functional codes have received much attention. In his PhD thesis, F.A.B. Edoukou investigated various functional codes linked to quadrics and Hermitian varieties defined in finite projective spaces (Edoukou, PhD Thesis, 2007). This work was continued in (Edoukou et al., Des Codes Cryptogr 56:219-233, 2010; Edoukou et al., J Pure Appl Algebr 214:1729-1739, 2010; Hallez and Storme, Finite Fields Appl 16:27-35, 2010), where the results of the thesis were improved and extended. In particular, Hallez and Storme investigated the functional codes , with a non-singular Hermitian variety in PG(N, q (2)). The codewords of this code are defined by evaluating the points of in the quadratic polynomials defined over . We now present the similar results for the functional code . The codewords of this code are defined by evaluating the points of a non-singular quadric in PG(N, q (2)) in the polynomials defining the Hermitian varieties of PG(N, q (2)).
Keywords
Hermitian varieties, code divisor, Functional codes, quadrics

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

MLA
Bartoli, Daniele et al. “On the Functional Codes Defined by Quadrics and Hermitian Varieties.” DESIGNS CODES AND CRYPTOGRAPHY 71.1 (2014): 21–46. Print.
APA
Bartoli, D., De Boeck, M., Fanali, S., & Storme, L. (2014). On the functional codes defined by quadrics and Hermitian varieties. DESIGNS CODES AND CRYPTOGRAPHY, 71(1), 21–46.
Chicago author-date
Bartoli, Daniele, Maarten De Boeck, Stefania Fanali, and Leo Storme. 2014. “On the Functional Codes Defined by Quadrics and Hermitian Varieties.” Designs Codes and Cryptography 71 (1): 21–46.
Chicago author-date (all authors)
Bartoli, Daniele, Maarten De Boeck, Stefania Fanali, and Leo Storme. 2014. “On the Functional Codes Defined by Quadrics and Hermitian Varieties.” Designs Codes and Cryptography 71 (1): 21–46.
Vancouver
1.
Bartoli D, De Boeck M, Fanali S, Storme L. On the functional codes defined by quadrics and Hermitian varieties. DESIGNS CODES AND CRYPTOGRAPHY. 2014;71(1):21–46.
IEEE
[1]
D. Bartoli, M. De Boeck, S. Fanali, and L. Storme, “On the functional codes defined by quadrics and Hermitian varieties,” DESIGNS CODES AND CRYPTOGRAPHY, vol. 71, no. 1, pp. 21–46, 2014.
@article{4351155,
  abstract     = {In recent years, functional codes have received much attention. In his PhD thesis, F.A.B. Edoukou investigated various functional codes linked to quadrics and Hermitian varieties defined in finite projective spaces (Edoukou, PhD Thesis, 2007). This work was continued in (Edoukou et al., Des Codes Cryptogr 56:219-233, 2010; Edoukou et al., J Pure Appl Algebr 214:1729-1739, 2010; Hallez and Storme, Finite Fields Appl 16:27-35, 2010), where the results of the thesis were improved and extended. In particular, Hallez and Storme investigated the functional codes , with a non-singular Hermitian variety in PG(N, q (2)). The codewords of this code are defined by evaluating the points of in the quadratic polynomials defined over . We now present the similar results for the functional code . The codewords of this code are defined by evaluating the points of a non-singular quadric in PG(N, q (2)) in the polynomials defining the Hermitian varieties of PG(N, q (2)).},
  author       = {Bartoli, Daniele and De Boeck, Maarten and Fanali, Stefania and Storme, Leo},
  issn         = {0925-1022},
  journal      = {DESIGNS CODES AND CRYPTOGRAPHY},
  keywords     = {Hermitian varieties,code divisor,Functional codes,quadrics},
  language     = {eng},
  number       = {1},
  pages        = {21--46},
  title        = {On the functional codes defined by quadrics and Hermitian varieties},
  url          = {http://dx.doi.org/10.1007/s10623-012-9712-4},
  volume       = {71},
  year         = {2014},
}

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