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List of publications

Preprints

[1] with Anna Gundert and Alberto Passuello, The theta number of simplicial complexes

[2] with Thomas Bellitto, Philippe Moustrou and Arnaud Pêcher, On the density of sets avoiding parallelohedron distance 1

[3] with Alain Couvreur and Gilles Zémor, Towards a function field version of Freiman's theorem

Journals

[39] with Oriol Serra and Gilles Zémor, Revisiting Kneser's theorem for field extensions Combinatorica (2017), published online

[38] with Oriol Serra and Gilles Zémor, An analogue of Vosper's theorem for extension fields , Mathematical Proceedings of the Cambridge Philosophical Society (2017), published online

[37] with Martin Ehler, Signal reconstruction from the magnitude of subspace components, IEEE Tansactions on Information Theory 61-7 (2015), 1-13.

[36] with Alberto Passuello and Alain Thiery, The density of sets avoiding distance 1 in Euclidean space Discrete and Computational Geometry, Vol. 53, Issue 4 (2015), 783-808.

[35] with Evan Decorte, Fernando Mario de Oliveira Filho, Frank Vallentin, Spectral bounds for the independence ratio and the chromatic number of an operator, Israel J. Math. 202 (2014), 227-254.

[34] C. Bachoc, M. Matolcsi, I.Z. Ruzsa, Squares and difference sets in finite fields, Integers vol.13 (2013).

[33] with Alberto Passuello and Frank Vallentin, Bounds for projective codes from semidefinite programming , Advances in Mathematics of Communications, Vol. 7, No. 2 (2013), 127-145.

[32] with Martin Ehler, Tight p-fusion frames , Appl. Comput. Harm. Anal. 35 (2013), 1-15.

[31] with Arnaud Pêcher, Alain Thiéry, On the theta number of powers of cycle graphs , Combinatorica, Vol. 33, No. 3 (2013), 297-317.

[30] with V. Chandar, Gérard Cohen, Patrick Solé, A. Tchamkerten, On Bounded Weight Codes, IEEE Trans. Inf. Th. 57-10 (2011).

[29] with Gilles Zémor, Bounds for binary codes relative to pseudo-distances of k points , Advances in Mathematics of Communications, Vol. 4, No. 4 (2010), 547-565.

[28] with Gabriele Nebe, Fernando Mário de Oliveira Filho, Frank Vallentin, Lower bounds for measurable chromatic numbers , Geom. Funct. Anal. 19 (2009), 645-661.

[27] with Frank Vallentin, Optimality and uniqueness of the (4,10,1/6) spherical code, Journal of Combinatorial Theory Series A 116 (2009), 195-204.

[26] with Frank Vallentin, Semidefinite programming, multivariate orthogonal polynomials, and codes in spherical caps, European Journal of Combinatorics 30 (3), special issue in the honor of Eiichi Bannai 60th birthday, (2009), 625-637.

[25] with Frank Vallentin, New upper bounds for kissing numbers from semidefinite programming , J. Amer. Math. Soc. 21 (2008), 909-924.

[24] with Yael Ben-Haim and Simon Litsyn, Bounds for codes in products of spaces, Grassmann and Stiefel manifolds, IEEE Trans. Inf. Th., 54-3 (2008), 1024-1035.

[23] with Riccardo Salvati-Manni, On Theta series vanishing at infinity and related lattices , Acta Arithmetica, 124-1 (2006), 59-71.

[22] Linear programming bounds for codes in Grassmannian spaces, IEEE Trans. Inf. Th., 52-5 (2006), 2111-2125.

[21] Designs, groups and lattices , J. Theor. Nombres Bordeaux 17 (2005), 25-44

[20] with E. Bannai and R. Coulangeon, Codes and Designs in Grassmannian spaces , Discrete Mathematics 277 (2004), 15-28

[19] with P. Gaborit Designs and self-dual codes with long shadows , J. Comb Th A 105(1) (2004), 15-34

[18] with G. Nebe and B. Venkov, Odd unimodular lattices of minimum 4. Acta Arithmetica 101 (2002), 151-158

[17] with G. Nebe, Zonal functions for the unitary groups and applications to hermitian lattices. Journal of Number Theory 96 (2002), 55-75

[16] with R. Coulangeon and G. Nebe, Designs in Grassmannian spaces and lattices. Journal of Algebraic Combinatorics 16 (2002), 5-19

[15] Harmonic weight enumerators of non-binary codes and MacWilliams identities AMS DIMACS, Series in discrete mathematics and theoretical computer science 56 (2001).

[14] with Boris Venkov: Modular forms, lattices and spherical designs dans ``Réseaux euclidiens, designs sphériques et groupes, J. Martinet, éd., L'Enseignement Mathématique, Monographie n. 37'', Genève (2001), 87-111

[13] with T.A. Gulliver, M. Harada Isodual codes over Z2k and isodual lattices J. Alg. Combin. 12 (2000), 223-240.

[12] with P. Gaborit On extremal additive GF(4)-codes of lengths 10 to 18 JTNB 12 (2000), 255-271

[11] On harmonic weight enumerators of binary codes Designs, Codes and Cryptography 18 (1999), 11-28.

[10] with Gabriele Nebe: Extremal lattices of minimum 8, related to the Mathieu $M_{22}$ J. Reine Angew. Math. 494 (1998)

[9] with Gabriele Nebe: Classification of two genera of 32-dimensional lattices over the Hurwitz order Exp. Maths 6-2 (1997) 151-162

[8] Applications of coding theory to the construction of modular lattices J. Comb. Th A 78-1 (1997) 92-119

[7] with Alexis Bonnecaze, Patrick Solé, Bernard Mourrain: Quaternary type II codes IEEE Trans. Inf. Th 43-3 (1997) 969-976

[6] Voisinage au sens de Kneser pour les réseaux quaternioniens Commentarii Mathematici Helvetici 70 (1995) 350-374

[5] C. Bachoc, Sur la structure hermitienne de la racine carrée de la codifférente, Annales de l'Institut Fourier 43-3 (1993), 619-654.

[4] C. Bachoc et C. Batut, Etude algorithmique de réseaux construits avec la forme Trace, Experimental Mathematics 1(3) (1992), 183-190.

[3] Sur les extensions de groupe de Galois A_4 tilda, Acta Arithmetica LXII.1 (1992), 869-884.

[2] C. Bachoc et B. Erez, Forme Trace et ramification sauvage, Proceeding of the London Mathematical Society 61 (1990), 209-226.

[1] C. Bachoc, Sur les réseaux unimodulaires pour Tr(x^2), Progr. Math., Séminaire de Théorie des Nombres 1988-1989 91, 1-11.

Book chapters

[1] with Dion C. Gijswijt, Alexander Schrijver, Frank Vallentin, Invariant semidefinite programs, in Handbook on Semidefinite, Conic and Polynomial Optimization (M.F. Anjos, J.B. Lasserre (ed.)), Springer 2012.

Conference proceedings

[1] Applications of semidefinite programming to coding theory (Proceedings of ITW 2010, Dublin).

[2] with Gabriele Nebe Siegel modular forms, Grassmannian designs, and unimodular lattices. , Proceedings of the Algebraic Combinatorics Conference (Kumamoto, 2002).

Lecture notes

[1] Semidefinite programming, harmonic analysis and coding theory, the lecture notes of a course given at the CIMPA summer school Semidefinite Programming in Algebraic Combinatorics , july 2009, updated June 2010.