Publications (22)
Numerical Techniques for Finding the Distances of Quantum Codes
Ilya Dumer, Alexey A. Kovalev, Leonid P. Pryadko
We survey the existing techniques for calculating code distances of classical codes and apply these techniques to generic quantum codes. For classical and quantum LDPC codes, we al…
Recursive Decoding and Its Performance for Low-Rate Reed-Muller Codes
Ilya Dumer
Recursive decoding techniques are considered for Reed-Muller (RM) codes of growing length and fixed order An algorithm is designed that has complexity of order a…
An elementary description of polarization process
Ilya Dumer
We analyze successive cancellation (SC) decoder by using two random functions. The first function is related to the likelihoods of 0 and 1 in each code position, while the second g…
Recursive decoding of Reed-Muller codes
Ilya Dumer
New soft- and hard decision decoding algorithms are presented for general Reed-Muller codes of length and distance . We…
On the Fingerprinting Capacity Under the Marking Assumption
N. Prasanth Anthapadmanabhan, Alexander Barg, Ilya Dumer
We address the maximum attainable rate of fingerprinting codes under the marking assumption, studying lower and upper bounds on the value of the rate for various sizes of the attac…
Duality and free energy analyticity bounds for few-body Ising models with extensive homology rank
Yi Jiang, Ilya Dumer, Alexey A. Kovalev +1
We consider pairs of few-body Ising models where each spin enters a bounded number of interaction terms (bonds), such that each model can be obtained from the dual of the other aft…