Alexander Barg: Selected Publications

                                       Subjects:
            [CG]
Codes on graphs [E] Extremal problems  [S] Secrecy generation
            [F]
Fingerprinting         [Q] Quantum codes     [CC] Combinatorial coding
            [S]
Surveys, popular    [N] Unclassfied

        Books edited:
 
·  Algebraic Coding Theory and Information Theory,  American Math. Soc. 2005 (vol. 68, AMS-DIMACS series).
 
·  Codes and Association Schemes, American Math. Soc.  2001 (vol. 56, AMS-DIMACS series).

       Papers:

· Bounds on sets with few distances, with Oleg Musin, arXiv:0905.2423 [E]
· On the number of errors correctable with codes on graphs, with Arya Mazumdar, preprint. [CG]
· Two-level fingerprinting codes, with N.P. Anthapadmanabhan, arXiv:0905:0417.  [F]
·
Bounds on ordered codes and orthogonal arrays, with Punarbasu Purkayastha, Moscow Mathematical Journal, to appear. arXiv:cs/0702033 [E]
·
 Weight distribution and decoding of codes on hypergraphs, with A. Mazumdar and G. Zémor, Advances in Math. of Communications, 2, 4, 2008, arXiv:0808.3453. [CG]
·
Performance analysis of soft decision decoding of Reed Solomon codes, with A. Duggan, IEEE Trans. Inform. Theory, 54, 2008, 5012–5018
· Fingerprinting capacity under the marking assumption, with N.P. Anthapadmanabhan and I. Dumer, IEEE Trans. Inform. Theory, June 2008. [F]
·
A functional view of upper bounds on codes, with D. Nogin, in book "Coding and Cryptology," edited by Y. Li et al., World Scientific, 2008, pp. 15-24, arXiv:0809.0091. (Proc. 1st Internat. Workshop, Wuyi Mountain, Fujian, China, June 2007). [E]
·
Codes in spherical caps, with Oleg Musin, Advances in Math. of Communications 1, 2007, 131-149. arXiv.org:math.MG/0606734 [E]
· Spectral approach to linear programming bounds on codes, with D.  Nogin, Problems of Information Transmission, 12, 2, 2006, 77-89, arXiv.org:cs.IT/0512025 [E]
· A bound on Grassmannian codes, with D. Yu. Nogin, Journal of Combinatorial Theory Ser. A 113, 8, 2006, 1629-1635 (Van Lint memorial issue). cs.IT/0512024 [E]
·
Distance properties of expander codes, with Gilles Zémor, IEEE Trans. Inform. Theory, Jan. 2006,  arXiv.org:cs.IT/0409010 [CG]
· Multilevel expander codes, with Gilles Zémor, in "Algebraic Coding Theory and Information Theory," American Math. Soc. 2005, pp. 69-83. (vol. 68, AMS-DIMACS series).  arXiv.org:cs.IT/0502079 [CG]
·
Distance distribution of binary codes and the error probability of decoding, with A. McGregor, IEEE Trans. Inform. Theory, Dec. 2005.  arXiv.org:cs.IT/0407011
·
Concatenated codes: serial and parallel, with Gilles Zémor, IEEE Trans. Inform. Theory, May 2005 [CG]
·
Improved bounds for the erasure/list scheme, IEEE Trans. Inform. Theory 2005.  arXiv.org:cs.IT/0407010
·
Error exponents of expander codes under linear-time decoding, with Gilles Zémor, SIAM J. Discrete Math., 2004. [CG]
·
A class of IPP codes with efficient identification, with G. Kabatiansky, Journal of Complexity, 2004. [F]
·
Improved bounds for list decoding of concatenated codes, with A. McGregor, preprint (2004).
·
Digital fingerprinting codes: Problem statements, constructions, identification of traitors, with G. R. Blakley and G. Kabatiansky, IEEE Trans. Inform. Theory, April 2003. [F]
·
Bounds on the covering radius of linear codes, with A. Ashikhmin, Designs, Codes and Cryptography, 27, 2002, pp. 261–269.
·
A low-rate bound on the reliability of a quantum discrete memoryless channel, IEEE Trans. Inform. Theory, Dec. 2002.
·
Bounds on packings of spheres in the Grassmann manifolds, with D. Yu. Nogin, IEEE Trans. Inform. Theory, Sept. 2002. [E]
·
Error exponents of expander codes, with Gilles Zémor, IEEE Trans. Inform. Theory, June 2002. [CG]
· Random codes: minimum distances and error exponents, with G. D. Forney, Jr. IEEE Trans. Inform. Theory 48 , 9, 2002, 2568-2573
·
On some polynomials related to the weight enumerator of linear codes, SIAM J. Discrete Math., 15, 2, 2002. [CC]
·
Extremal problems of coding theory, in book: H. Niederreiter, Editor, "Coding Theory and Cryprography," World Scientific, 2002, pp. 1-48. (Notes of lectures at the Institute for Math. Sciences of the University of Singapore, Sept. 2001) [S,E]
·
Estimates of the distance distribution of nonbinary codes, with applications, with A. Ashikhmin and S. Litsyn, Codes and Association Schemes, AMS., Providence, RI (2001), pp. 287-303 [E]
· Estimates of the distance distribution of codes and designs, with A. Ashikhmin and S. Litsyn, IEEE Trans. Inform. Theory, March 2001, 1050-1061. [E]
· A hypergraph approach to IPP codes: the case of multiple parents, joint with G. Cohen, S. Encheva, G. Kabatisanky and G. Zémor, SIAM J. Discrete Math., Nov. 2001. [F]
·
Linear codes with exponentially many light vectors, Journal of Combinatorial Theory Series A, 96, no. 2, 2001, 396-399. [N]
· Concatenated codes with fixed inner codes and random outer codes, with J. Justesen and C. Thommesen, IEEE Trans. Inform. Theory, Jan. 2001.
·
A new upper bound on codes decodable into size-2 lists, with A. Ashikhmin and S. Litsyn, in Numbers, Information and Complexity, Ingo Althoefer et al., Eds. , Boston: Kluwer Publ., 2000, pp. 239-244
·
Strengthening the Varshamov-Gilbert bound, with S. Guritman and J. Simonis, Linear Algebra and Applications, 307 (2000), 119-129. [E]
· Quantum error detection II, IEEE Trans. Inform. Theory, May 2000, pp. 789-800.
· Quantum error detection I, IEEE Trans. Inform. Theory, May 2000, pp. 778-788.
·
A new upper bound on the reliability function of the Gaussian channel, with A. Ashikhmin and S. Litsyn, IEEE Trans. Inform. Theory, 1999.
·
Linear-time binary codes correcting localized erasures, with S. Zhou, IEEE Trans. Inform. Theory, 45, no. 7, 1999, 2547-2552.
·
The complexity of minimum distance decoding of long linear codes, with E. Krouk and H.C.A.van Tilborg, IEEE Trans. Inform. Theory, 45, no. 5 (1999), 1392-1405
· New upper bounds on generalized weights, with A. Ashikhmin and S. Litsyn, IEEE Trans. Inform. Theory, 45, no. 4 , 1999.
· Binomial moments of the distance distribution: Bounds and applications, with A. Ashikhmin, IEEE Trans. Inform. Theory, 45, no. 2, 1999.
· Binomial moments of the distance distribution and the probability of undetected error, with A. Ashikhmin, Designs, Codes and Cryptography, 1999. [CC]
· A quantum decoding algorithm of the simplex code, with S. Zhou, Allerton conference, about 1998. [Q]
· Complexity issues in coding theory, in book: Handbook of Coding Theory, vol. 1, Elsevier Science, 1998, pp. 649-754 [S]
· Minimal vectors in linear codes, with A. Ashikhmin, IEEE Trans. Inform. Theory,1998. [CC]
· The matroid of supports of a linear code, Applicable Algebra Eng. Commun. Comput., 8, 1997. [CC]
· Two families of low-correlated binary sequences, Applicable Algebra Eng. Commun. Comput., 7, no. 6, 1996, 433-438.
· Some new NP complete coding problems, Probl. Inform. Trans., 30, no. 3, 1994, pp.23-28.
· At the dawn of the theory of codes, The Mathematical Intelligencer, 15, 1, 1993, 20-26. [S]
· On computing the weight spectrum of cyclic codes, with I. Dumer, IEEE Trans. Inform. Theory, 1992. [CC]
· What is the Fortune, Kvant 9 (1990) (in Russian). [S]
·
Algebrogeometric codes from curves of small genus, with G. Katsman and M. Tsfasman, Probl. Inform. Trans., 23, no. 1, 1987, 42-46,
· Algorithm
of cascaded decoding with incomplete inspection of code vectors, with I. Dumer, Probl. Inform. Trans. 22, no. 1, 1986, 3-8.