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REPORTS > AUTHORS > OMAR ALRABIAH:
All reports by Author Omar Alrabiah:

TR22-101 | 15th July 2022
Omar Alrabiah, Venkatesan Guruswami, Pravesh Kothari, Peter Manohar

A Near-Cubic Lower Bound for 3-Query Locally Decodable Codes from Semirandom CSP Refutation

A code $C \colon \{0,1\}^k \to \{0,1\}^n$ is a $q$-locally decodable code ($q$-LDC) if one can recover any chosen bit $b_i$ of the message $b \in \{0,1\}^k$ with good confidence by randomly querying the encoding $x = C(b)$ on at most $q$ coordinates. Existing constructions of $2$-LDCs achieve $n = ... more >>>


TR22-082 | 27th May 2022
Omar Alrabiah, Eshan Chattopadhyay, Jesse Goodman, Xin Li, João Ribeiro

Low-Degree Polynomials Extract from Local Sources

We continue a line of work on extracting random bits from weak sources that are generated by simple processes. We focus on the model of locally samplable sources, where each bit in the source depends on a small number of (hidden) uniformly random input bits. Also known as local sources, ... more >>>


TR21-145 | 19th October 2021
Omar Alrabiah, Venkatesan Guruswami

Revisiting a Lower Bound on the Redundancy of Linear Batch Codes

A recent work of Li and Wootters (2021) shows a redundancy lower bound of $\Omega(\sqrt{Nk})$ for systematic linear $k$-batch codes of block length $N$ by looking at the $O(k)$ tensor power of the dual code. In this note, we present an alternate proof of their result via a linear independence ... more >>>


TR21-119 | 13th August 2021
Omar Alrabiah, Venkatesan Guruswami

Visible Rank and Codes with Locality

Revisions: 1

We propose a framework to study the effect of local recovery requirements of codeword symbols on the dimension of linear codes, based on a combinatorial proxy that we call "visible rank." The locality constraints of a linear code are stipulated by a matrix $H$ of $\star$'s and $0$'s (which we ... more >>>


TR19-005 | 16th January 2019
Omar Alrabiah, Venkatesan Guruswami

An Exponential Lower Bound on the Sub-Packetization of MSR Codes

Revisions: 1

An $(n,k,\ell)$-vector MDS code is a $\mathbb{F}$-linear subspace of $(\mathbb{F}^\ell)^n$ (for some field $\mathbb{F}$) of dimension $k\ell$, such that any $k$ (vector) symbols of the codeword suffice to determine the remaining $r=n-k$ (vector) symbols. The length $\ell$ of each codeword symbol is called the sub-packetization of the code. Such a ... more >>>




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