Selected publications

Nonbinary codes

I. Dumer, 1995. Nonbinary double-error-correcting codes designed by means of algebraic varieties. IEEE Trans. Inform. Theory, vol. 41, no. 6, pp. 1550-1560.

S. Yekhanin and I. Dumer, 2004. Long nonbinary codes exceeding the Gilbert Varshamov bound for any fixed distance,” IEEE Trans. Info. Theory, vol. 50, no. 10, pp. 2357-2362.

Concatenated design

I. Dumer, 1998. Concatenated codes and their generalizations. Chapter 23, pp. 1911-1988. In: V. S. Pless and W. C. Huffman (eds.), Handbook of Coding Theory, Elsevier Science, Amsterdam.

Near-optimum decoding

I. Dumer, 1996. Suboptimal decoding of linear codes: Partition technique. IEEE Trans. Inform. Theory, vol. 42, no. 6, pp. 1971-1986.

I. Dumer, 1999. Sort-and-match algorithm for soft decision decoding. IEEE Trans. Inform. Theory, vol. 45, no. 7, pp. 2233-2338.

I. Dumer, 2001. Soft decision decoding using punctured codes. IEEE Trans. Inform Theory, vol. 47, no. 1, pp. 59-71, 2001.

Complexity. Maximum likelihood decoding

I. Dumer, 2000. Ellipsoidal lists and maximum likelihood decoding. IEEE Trans. Inform. Theory, vol. 46, no. 2, pp. 649-656.

I. Dumer, D. Micciancio, and M. Sudan, 2003. Hardness of Approximating the Minimum Distance of a Linear Code. IEEE Trans. Inform. Theory, Vol. 49, no. 1, pp. 22-37.

Majority and recursive decoding for Reed-Muller codes

I. Dumer and R. Krichevskiy, 2000. Soft decision majority decoding of Reed-Muller codes. IEEE Trans. Info. Theory, vol. 46, no. 1, pp. 258-264.

I. Dumer, 2004. “Recursive decoding and its performance for low-rate Reed-Muller codes,” IEEE Trans.Info. Theory, vol. 50, no. 5, pp. 811-823.

I. Dumer, 2006. “Soft decision decoding of Reed-Muller codes: a simplified algorithm,'' IEEE Trans. Info. Theory, vol. 52, no. 3, 954-963.

I. Dumer and K. Shabunov, 2006. “Soft decision decoding of Reed-Muller codes: recursive lists,'' IEEE Trans. Info. Theory, vol. 52, no. 3, 1260-1266.

M. Burnashev and I. Dumer, 2006. “Error Exponents for Recursive Decoding of Reed-Muller Codes on a Binary-Symmetric Channel,” IEEE Trans. Info. Theory, vol. 52, no. 11, 4880-4891

M. Burnashev and I. Dumer, 2008. “Error Exponents for two soft-decision decoding algorithms of Reed-Muller Codes,” to be submitted.

Spheres and Ellipsoids in the Hamming and Euclidean spaces

I. Dumer, M. Pinsker, and V. Prelov, 2002. ''Epsilon–entropy of an ellipsoid in a Hamming space'', Probl. Info. Transmission, vol. 38, 1–15.

I. Dumer, M. Pinsker, and V. Prelov, 2002. ''An optimization problem related to the computation of the epsilon–entropy of an ellipsoid in a Hamming space'', Probl. Info. Transmission, vol. 38, 99–112.

I. Dumer, M. Pinsker, and V. Prelov, 2004. “On coverings of ellipsoids in Euclidean spaces,” IEEE Trans. Info. Theory, vol. 50, no. 10, pp. 2348-2356.

I. Dumer, M. Pinsker, and V. Prelov, 2006. “On the thinnest coverings of spheres and ellipsoids with balls in Hamming and Euclidean spaces,” Lecture notes in Computer Science, vol. 4123, 883 – 910.

I. Dumer, 2006. ''Covering an ellipsoid with equal balls,'' Journal of Combinatorial Theory A, vol. 113, 1667–1676.

I. Dumer, 2007. ''Covering spheres with spheres,'' Discrete and Computational Geometry.

Quantum error correction

E. Brion, G. Harel, N. Kebaili, V.M. Akulin, and I. Dumer, 2004 “Coherence Protection by the Zeno effect,” Europhysics Letters, vol. 66, no. 2, pp. 157-163.

E. Brion, V. M. Akulin, I. Dumer, G. Harel, G. Kurizki, 2005 “Coherence Protection by random coding, J. Optics B: Quantum and Semiclassical Optics, vol. 7, S1--S3.