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Electronic Colloquium on Computational Complexity

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Reports tagged with Algebraic coding:
TR13-060 | 10th April 2013
Venkatesan Guruswami, Swastik Kopparty

Explicit Subspace Designs

A subspace design is a collection $\{H_1,H_2,\dots,H_M\}$ of subspaces of ${\mathbf F}_q^m$ with the property that no low-dimensional subspace $W$ of ${\mathbf F}_q^m$ intersects too many subspaces of the collection. Subspace designs were introduced by Guruswami and Xing (STOC 2013) who used them to give a randomized construction of optimal ... more >>>

TR13-170 | 2nd December 2013
Venkatesan Guruswami, Carol Wang

Explicit rank-metric codes list-decodable with optimal redundancy

We construct an explicit family of linear rank-metric codes over any field ${\mathbb F}_h$ that enables efficient list decoding up to a fraction $\rho$ of errors in the rank metric with a rate of $1-\rho-\epsilon$, for any desired $\rho \in (0,1)$ and $\epsilon > 0$. Previously, a Monte Carlo construction ... more >>>

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