5 citations · 13 across the 9 of their papers we have counts for
10 papers
Comments on the recent improvements of the MRRW bounds
Alexander Barg
The asymptotic McEliece--Rodemich--Rumsey--Welch bound (1977) limits the largest attainable rate of binary codes as a function of the relative distance. After a nearly half-century…
Universally optimal (wiretap) codes
Madhura Pathegama, Alexander Barg
Universally optimal (UO) codes were introduced by H. Cohn and A. Kumar in 2007 and later extended to the discrete setting by Cohn and Y. Zhao. They minimize the ``energy'' among al…
Minimum distance and decoding of Coxeter codes
Alexander Barg, Qëndrim R. Gashi, Tianyuan Xu
A binary Coxeter code associated with a finite Coxeter system is an -linear span of indicators of standard cosets of a fixed rank. Coxeter codes, introduced…
Regular LDPC codes on BMS wiretap channels: Security bounds
Madhura Pathegama, Alexander Barg
We improve the secrecy guarantees for transmission over general binary memoryless symmetric wiretap channels that relies on regular LDPC codes. Previous works showed that LDPC code…
Coxeter codes: Extending the Reed-Muller family
Nolan J. Coble, Alexander Barg
Binary Reed-Muller (RM) codes are defined via evaluations of Boolean-valued functions on . We introduce a class of binary linear codes that generalizes the RM famil…
Geometric structure and transversal logic of quantum Reed-Muller codes
Alexander Barg, Nolan J. Coble, Dominik Hangleiter +1
Designing efficient and noise-tolerant quantum computation protocols generally begins with an understanding of quantum error-correcting codes and their native logical operations. T…
Rényi divergence-based uniformity guarantees for -universal hash functions
Madhura Pathegama, Alexander Barg
Universal hash functions map the output of a source to random strings over a finite alphabet, aiming to approximate the uniform distribution on the set of strings. A classic result…
Limitations of the decoding-to-LPN reduction via code smoothing
Madhura Pathegama, Alexander Barg
The Learning Parity with Noise (LPN) problem underlines several classic cryptographic primitives. Researchers have attempted to demonstrate the algorithmic hardness of this problem…
Generalized regenerating codes and node repair on graphs
Adway Patra, Alexander Barg
We consider regenerating codes in distributed storage systems where connections between the nodes are constrained by a graph. In this problem, the failed node downloads the informa…
Rényi divergence guarantees for hashing with linear codes
Madhura Pathegama, Alexander Barg
We consider the problem of distilling uniform random bits from an unknown source with a given -entropy using linear hashing. As our main result, we estimate the expected -div…