5 papers
Binary code rate bounds via classical--quantum channels
Omar Alrabiah, Venkatesan Guruswami
We derive the four principal asymptotic rate-distance tradeoffs for binary codes---Plotkin, Elias--Bassalygo, and the two McEliece--Rodemich--Rumsey--Welch (MRRW) bounds---from one…
No low-degree tests for quantum states
Omar Alrabiah, Srinivasan Arunachalam, Sabee Grewal +1
We study the problem of testing low-degree phase states, namely m-qudit quantum states of the form , where is a degree- p…
Random Reed-Solomon Codes Achieve List-Decoding Capacity With Linear-Sized Alphabets
Omar Alrabiah, Zeyu Guo, Venkatesan Guruswami +2
Reed-Solomon codes are a classic family of error-correcting codes consisting of evaluations of low-degree polynomials over a finite field on some sequence of distinct field element…
Low-Degree Polynomials Are Good Extractors
Omar Alrabiah, Jesse Goodman, Jonathan Mosheiff +1
We prove that random low-degree polynomials (over ) are unbiased, in an extremely general sense. That is, we show that random low-degree polynomials are good randomne…
Ideal Pseudorandom Codes
Omar Alrabiah, Prabhanjan Ananth, Miranda Christ +2
Pseudorandom codes are error-correcting codes with the property that no efficient adversary can distinguish encodings from uniformly random strings. They were recently introduced b…