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Electronic Colloquium on Computational Complexity

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Reports tagged with Reed-Muller code:
TR02-020 | 13th March 2002
Elizaveta Okol'nishnikova

On one lower bound for branching programs

The method of obtaining lower bounds on the complexity
of Boolean functions for nondeterministic branching programs
is proposed.
A nonlinear lower bound on the complexity of characteristic
functions of Reed--Muller codes for nondeterministic
branching programs is obtained.

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TR13-175 | 6th December 2013
Venkatesan Guruswami, Chaoping Xing

Hitting Sets for Low-Degree Polynomials with Optimal Density

Revisions: 1

We give a length-efficient puncturing of Reed-Muller codes which preserves its distance properties. Formally, for the Reed-Muller code encoding $n$-variate degree-$d$ polynomials over ${\mathbb F}_q$ with $q \ge \Omega(d/\delta)$, we present an explicit (multi)-set $S \subseteq {\mathbb F}_q^n$ of size $N=\mathrm{poly}(n^d/\delta)$ such that every nonzero polynomial vanishes on at most ... more >>>

TR15-158 | 27th September 2015
Ofer Grossman, Dana Moshkovitz

Amplification and Derandomization Without Slowdown

We present techniques for decreasing the error probability of randomized algorithms and for converting randomized algorithms to deterministic (non-uniform) algorithms. Unlike most existing techniques that involve repetition of the randomized algorithm, and hence a slowdown, our techniques produce algorithms with a similar run-time to the original randomized algorithms.

The ... more >>>

TR20-142 | 15th September 2020
Vahid Reza Asadi, Igor Shinkar

Relaxed Locally Correctable Codes with Improved Parameters

Locally decodable codes (LDCs) are error-correcting codes $C : \Sigma^k \to \Sigma^n$ that admit a local decoding algorithm that recovers each individual bit of the message by querying only a few bits from a noisy codeword. An important question in this line of research is to understand the optimal trade-off ... more >>>

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