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A central problem in the theory of algorithms for data streams is to determine which functions on a stream can be approximated in sublinear, and especially sub-polynomial or poly-logarithmic, space. Given a function $g$, we study the space…
We prove new lower bounds for locally decodable codes and private information retrieval. We show that a 2-query LDC encoding n-bit strings over an l-bit alphabet, where the decoder only uses b bits of each queried position of the codeword,…
For quantum algorithms for problems in which the task is to compute an entire field of values, like e.g. computational fluid dynamics (CFD), it is often proposed amplitude encoding w.r.t. multiple qubits; however, the efforts implied by it…
We describe a new class of list decodable codes based on Galois extensions of function fields and present a list decoding algorithm. These codes are obtained as a result of folding the set of rational places of a function field using…
Service rate is an important, recently introduced, performance metric associated with distributed coded storage systems. Among other interpretations, it measures the number of users that can be simultaneously served by the storage system.…
Computing nonlinear functions over multilinear forms is a general problem with applications in risk analysis. For instance in the domain of energy economics, accurate and timely risk management demands for efficient simulation of millions…
Inspired by mobile satellite communication systems and the important and prevalent applications of computational tasks, we consider a distributed source coding model for compressing vector-linear functions, which consists of multiple…
Decoding a Reed-Solomon code can be modeled by a bilinear system which can be solved by Gr\"obner basis techniques. We will show that in this particular case, these techniques are much more efficient than for generic bilinear systems with…
The length function $\ell_q(r,R)$ is the smallest length of a $q$-ary linear code of codimension (redundancy) $r$ and covering radius $R$. The $d$-length function $\ell_q(r,R,d)$ is the smallest length of a $q$-ary linear code with…
In the index coding problem, introduced by Birk and Kol (INFOCOM, 1998), the goal is to broadcast an n bit word to n receivers (one bit per receiver), where the receivers have side information represented by a graph G. The objective is to…
Polynomial approximations to boolean functions have led to many positive results in computer science. In particular, polynomial approximations to the sign function underly algorithms for agnostically learning halfspaces, as well as…
The issue of repairing Reed-Solomon codes currently employed in industry has been sporadically discussed in the literature. In this work we carry out a systematic study of these codes and investigate important aspects of repairing them…
A major open problem in communication complexity is whether or not quantum protocols can be exponentially more efficient than classical protocols on _total_ Boolean functions in the two-party interactive model. The answer appears to be…
We construct $s$-interleaved linearized Reed--Solomon (ILRS) codes and variants and propose efficient decoding schemes that can correct errors beyond the unique decoding radius in the sum-rank metric. The proposed interpolation-based scheme…
Linearized Reed-Solomon (LRS) codes are sum-rank metric codes that fulfill the Singleton bound with equality. In the two extreme cases of the sum-rank metric, they coincide with Reed-Solomon codes (Hamming metric) and Gabidulin codes (rank…
Simulation of fermionic Hamiltonians with gate-based quantum computers requires the selection of an encoding from fermionic operators to quantum gates, the most widely used being the Jordan-Wigner transform. Many alternative encodings…
This paper studies the parameters for which Reed-Muller (RM) codes over $GF(2)$ can correct random erasures and random errors with high probability, and in particular when can they achieve capacity for these two classical channels.…
We investigate the dividing line between classical and quantum computational power in estimating properties of matrix functions. More precisely, we study the computational complexity of two primitive problems: given a function $f$ and a…
Research on quantum computing has recently gained significant momentum since first physical devices became available. Many quantum algorithms make use of so-called oracles that implement Boolean functions and are queried with highly…
Coded computing has emerged as a promising framework for tackling significant challenges in large-scale distributed computing, including the presence of slow, faulty, or compromised servers. In this approach, each worker node processes a…