Vanishing ideals of projective spaces over nite elds and a projective footprint bound, Acta Mathematica Sinica, English Series, vol.35, issue.1, p.4763, 2019. ,
Evaluation codes from smooth quadric surfaces and twisted Segre varieties, Des. Codes Cryptogr, vol.66, issue.1-3, p.291303, 2013. ,
URL : https://hal.archives-ouvertes.fr/inria-00611801
Undergraduate Texts in Mathematics ,
Toric varieties, Graduate Studies in Mathematics, vol.124, 2011. ,
Projective Reed-Muller type codes on rational normal scrolls, Finite Fields Appl, vol.37, p.37, 2016. ,
A global view of residues in the torus, Algorithms for algebra, vol.117, pp.119-144, 1996. ,
Evaluation codes from smooth quadric surfaces and twisted Segre varieties, Des. Codes Cryptogr, vol.66, issue.1-3, pp.291-303, 2013. ,
URL : https://hal.archives-ouvertes.fr/inria-00611801
Toric varieties, Graduate Studies in Mathematics, vol.124, 2011. ,
Projective Reed-Muller type codes on rational normal scrolls, Finite Fields Appl, vol.37, pp.85-107, 2016. ,
An introduction to algebraic geometry, Notes written with the collaboration of Richard Weiss, 1989. ,
Polar curves, J. Algebra, vol.181, issue.2, pp.449-477, 1996. ,
Around Sziklai's conjecture on the number of points of a plane curve over a finite field, Finite Fields Appl, vol.15, issue.4, pp.468-474, 2009. ,
Sziklai's conjecture on the number of points of a plane curve over a finite field II, Finite fields: theory and applications, vol.518, pp.225-234, 2010. ,
Sziklai's conjecture on the number of points of a plane curve over a finite field III, Finite Fields Appl, vol.16, issue.5, pp.315-319, 2010. ,
A bound on the number of points of a curve in a projective space over a finite field, Theory and applications of finite fields, vol.579, pp.103-110, 2012. ,
Algebraic geometric codes on minimal hirzebruch surfaces, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01842416
Chapters on algebraic surfaces, Complex algebraic geometry, vol.3, pp.3-159, 1993. ,
Weierstrass points and curves over finite fields, Proc. London Math. Soc, vol.52, issue.3, pp.1-19, 1986. ,
E-mail address: jade.nardi@math.univ-toulouse.fr INSTITUT DE MATHÉMATIQUES DE TOULOUSE ; UMR 5219, Topics in algebraic and noncommutative geometry, vol.324, pp.219-226, 2001. ,
, Hence, ev F 2 q (X i Y j ) lies in Lift ? RS q (d) if, for all u ? ?(j, ?), every monomial T i+u evaluates to a codeword of RS q (d). and only if T a = T b mod (T q ? T)
, Let d ? q ? 2. A pair (i, j) ? [0, d] 2 belongs to D(q, d, ?) if and only if for every k ? N ? such that for all r ? 0, |k (r) | ? j (r)
Hypersurfaces in Weighted Projective Spaces Over Finite Fields with Applications to Coding Theory, notation mod * q is used in [GKS13], but we find it quite unconvenient 14 112 CHAPITRE 5. PIR ET LIFT References, pp.25-61, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01478729
A storageefficient and robust private information retrieval scheme allowing few servers, Cryptology and Network Security -13th International Conference, CANS 2014, Heraklion, vol.8813, pp.222-239, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01094807
Breaking the O(n 1/(2k?1) ) Barrier for Information-Theoretic Private Information Retrieval, 43rd Symposium on Foundations of Computer Science (FOCS 2002), pp.261-270, 2002. ,
Robust information-theoretic private information retrieval, Security in Communication Networks, Third International Conference, vol.2576, pp.326-341, 2002. ,
Private Information Retrieval, 36th Annual Symposium on Foundations of Computer Science, pp.41-50, 1995. ,
2-Server PIR with Subpolynomial Communication, J. ACM, vol.63, issue.4, 2016. ,
3-Query Locally Decodable Codes of Subexponential Length, SIAM J. Comput, vol.41, issue.6, pp.1694-1703, 2012. ,
Private Information Retrieval from Coded Databases with Colluding Servers, SIAM J. Appl. Algebra Geometry, vol.1, issue.1, pp.647-664, 2017. ,
New Affine-Invariant Codes from Lifting, Theoretical Computer Science, ITCS '13, pp.529-540, 2013. ,
Weighted Reed-Muller codes revisited, Des. Codes Cryptogr, vol.66, issue.1-3, pp.195-220, 2013. ,
High-Rate Locally Correctable Codes via Lifting, IEEE Trans. Information Theory, vol.62, issue.12, pp.6672-6682, 2016. ,
Private Information Retrieval in Distributed Storage Systems using an Arbitrary Linear Code, 2017 IEEE International Symposium on Information Theory, pp.1421-1425, 2017. ,
On the Efficiency of Local Decoding Procedures for Error-Correcting Codes, Proceedings of the Thirty-Second Annual ACM Symposium on Theory of Computing, pp.80-86, 2000. ,
Codes with locality: constructions and applications to cryptographic protocols, 2018. ,
URL : https://hal.archives-ouvertes.fr/tel-01951078
Lifted Projective Reed-Solomon Codes. Designs, Codes and Cryptography, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01901147
Théorie des Fonctions Numériques Simplement Périodiques, American Journal of Mathematics, vol.1, issue.3, pp.197-240, 1878. ,
Weighted Reed-Muller codes and algebraic-geometric codes, IEEE Trans. Inform. Theory, vol.38, issue.6, pp.1821-1826, 1992. ,
One Extra Bit of Download Ensures Perfectly Private Information Retrieval, IEEE International Symposium on Information Theory, pp.856-860, 2014. ,
Private information retrieval from MDS coded data in distributed storage systems, IEEE Trans. Information Theory, vol.64, issue.11, pp.7081-7093, 2018. ,
Towards 3-query Locally Decodable Codes of Subexponential Length, J. ACM, vol.55, issue.1, pp.1-1, 2008. ,
, Locally Decodable Codes. Foundations and Trends in Theoretical Computer Science, vol.6, issue.3, p.27, 2012.