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Electronic Colloquium on Computational Complexity

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TR22-029 | 27th February 2022
Anthony Leverrier, Gilles Zémor

Quantum Tanner codes

Revisions: 2

Tanner codes are long error correcting codes obtained from short codes and a graph, with bits on the edges and parity-check constraints from the short codes enforced at the vertices of the graph. Combining good short codes together with a spectral expander graph yields the celebrated expander codes of Sipser ... more >>>


TR22-028 | 23rd February 2022
Dan Karliner, Roie Salama, Amnon Ta-Shma

The plane test is a local tester for Multiplicity Codes

Multiplicity codes are a generalization of RS and RM codes where for each evaluation point we output the evaluation of a low-degree polynomial and all of its directional derivatives up to order $s$. Multi-variate multiplicity codes are locally decodable with the natural local decoding algorithm that reads values on a ... more >>>


TR22-027 | 22nd February 2022
Guy Blanc, Dean Doron

New Near-Linear Time Decodable Codes Closer to the GV Bound

Revisions: 1

We construct a family of binary codes of relative distance $\frac{1}{2}-\varepsilon$ and rate $\varepsilon^{2} \cdot 2^{-\log^{\alpha}(1/\varepsilon)}$ for $\alpha \approx \frac{1}{2}$ that are decodable, probabilistically, in near linear time. This improves upon the rate of the state-of-the-art near-linear time decoding near the GV bound due to Jeronimo, Srivastava, and Tulsiani, who ... more >>>



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