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Electronic Colloquium on Computational Complexity

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Reports tagged with linear functions:
TR96-029 | 16th April 1996
Alexander E. Andreev, Andrea E. F. Clementi, Jose' D. P. Rolim

Towards efficient constructions of hitting sets that derandomize BPP

The efficient construction of Hitting Sets for non trivial classes
of boolean functions is a fundamental problem in the theory
of derandomization. Our paper presents a new method to efficiently
construct Hitting Sets for the class of systems of boolean linear
functions. Systems of boolean linear functions ... more >>>

TR24-056 | 29th March 2024
Prashanth Amireddy, Amik Raj Behera, Manaswi Paraashar, Srikanth Srinivasan, Madhu Sudan

Local Correction of Linear Functions over the Boolean Cube

Revisions: 1

We consider the task of locally correcting, and locally list-correcting, multivariate linear functions over the domain $\{0,1\}^n$ over arbitrary fields and more generally Abelian groups. Such functions form error-correcting codes of relative distance $1/2$ and we give local-correction algorithms correcting up to nearly $1/4$-fraction errors making $\widetilde{\mathcal{O}}(\log n)$ queries. This ... more >>>

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