Related papers: Weighted Lifted Codes: Local Correctabilities and …
In this paper, we introduce curve-lifted codes over fields of arbitrary characteristic, inspired by Hermitian-lifted codes over $\mathbb{F}_{2^r}$. These codes are designed for locality and availability, and their particular parameters…
A \emph{private proximity retrieval} (\emph{PPR}) scheme is a protocol which allows a user to retrieve the identities of all records in a database that are within some distance $r$ from the user's record $x$. The user's \emph{privacy} at…
Private Information Retrieval (PIR), despite being well studied, is computationally costly and arduous to scale. We explore lower-cost relaxations of information-theoretic PIR, based on dummy queries, sparse vectors, and compositions with…
Short-length Reed--Muller codes under majority-logic decoding are of particular importance for efficient hardware implementations in real-time and embedded systems. This paper significantly improves Chen's two-step majority-logic decoding…
A generator matrix of a linear code $\C$ over $\gf(q)$ is also a matrix of the same rank $k$ over any extension field $\gf(q^\ell)$ and generates a linear code of the same length, same dimension and same minimum distance over $\gf(q^\ell)$,…
Distributed storage systems for large clusters typically use replication to provide reliability. Recently, erasure codes have been used to reduce the large storage overhead of three-replicated systems. Reed-Solomon codes are the standard…
Algebraic decoding algorithms are commonly applied for the decoding of Reed-Solomon codes. Their main advantages are low computational complexity and predictable decoding capabilities. Many algorithms can be extended for correction of both…
We consider the problem of designing private information retrieval (PIR) schemes on data of $m$ files replicated on $n$ servers that can possibly collude. We focus on devising robust PIR schemes that can tolerate stragglers, i.e., slow or…
In the classical private information retrieval (PIR) setup, a user wants to retrieve a file from a database or a distributed storage system (DSS) without revealing the file identity to the servers holding the data. In the quantum PIR (QPIR)…
Linear codes have diverse applications in secret sharing schemes, secure two-party computation, association schemes, strongly regular graphs, authentication codes and communication. There are a large number of linear codes with few weights…
Modern distributed computation infrastructures are often plagued by unavailabilities such as failing or slow servers. These unavailabilities adversely affect the tail latency of computation in distributed infrastructures. The simple…
In this article, we present a new construction of evaluation codes in the Hamming metric, which we call twisted Reed-Solomon codes. Whereas Reed-Solomon (RS) codes are MDS codes, this need not be the case for twisted RS codes. Nonetheless,…
Good quantum error-correcting codes that fulfill practical considerations, such as simple encoding circuits and efficient decoders, are essential for functional quantum information processing systems. Quantum polar codes satisfy some of…
Distributed storage systems must handle both data heterogeneity, arising from non-uniform access demands, and device heterogeneity, caused by time-varying node reliability. In this paper, we study convertible codes, which enable the…
We consider the problem of designing PIR scheme on coded data when certain nodes are unresponsive. We provide the construction of $\nu$-robust PIR schemes that can tolerate up to $\nu$ unresponsive nodes. These schemes are adaptive and…
Reed-Muller codes consist of evaluations of $n$-variate polynomials over a finite field $\mathbb{F}$ with degree at most $d$. Much like every linear code, Reed-Muller codes can be characterized by constraints, where a codeword is valid if…
Separating codes have their applications in collusion-secure fingerprinting for generic digital data, while they are also related to the other structures including hash family, intersection code and group testing. In this paper we study…
Private information retrieval (PIR) gets renewed attentions due to its information-theoretic reformulation and its application in distributed storage system (DSS). The general PIR model considers a coded database containing $N$ servers…
In this work, we show new and improved error-correcting properties of folded Reed-Solomon codes and multiplicity codes. Both of these families of codes are based on polynomials over finite fields, and both have been the sources of recent…
New soft- and hard decision decoding algorithms are presented for general Reed-Muller codes $\left\{\genfrac{}{}{0pt}{}{m}{r}\right\} $ of length $2^{m}$ and distance $2^{m-r}$. We use Plotkin $(u,u+v)$ construction and decompose code…