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REPORTS > AUTHORS > SIDDHARTH BHANDARI:
All reports by Author Siddharth Bhandari:

TR21-036 | 14th March 2021
Siddharth Bhandari, Prahladh Harsha, Mrinal Kumar, Madhu Sudan

Ideal-theoretic Explanation of Capacity-achieving Decoding

In this work, we present an abstract framework for some algebraic error-correcting codes with the aim of capturing codes that are list-decodable to capacity, along with their decoding algorithm. In the polynomial ideal framework, a code is specified by some ideals in a polynomial ring, messages are polynomials and their ... more >>>


TR20-179 | 2nd December 2020
Siddharth Bhandari, Prahladh Harsha, Mrinal Kumar, Madhu Sudan

Decoding Multivariate Multiplicity Codes on Product Sets

The multiplicity Schwartz-Zippel lemma bounds the total multiplicity of zeroes of a multivariate polynomial on a product set. This lemma motivates the multiplicity codes of Kopparty, Saraf and Yekhanin [J. ACM, 2014], who showed how to use this lemma to construct high-rate locally-decodable codes. However, the algorithmic results about these ... more >>>


TR20-019 | 19th February 2020
Siddharth Bhandari, Prahladh Harsha

A note on the explicit constructions of tree codes over polylogarithmic-sized alphabet

Recently, Cohen, Haeupler and Schulman gave an explicit construction of binary tree codes over polylogarithmic-sized output alphabet based on Pudl\'{a}k's construction of maximum-distance-separable (MDS) tree codes using totally-non-singular triangular matrices. In this short note, we give a unified and simpler presentation of Pudl\'{a}k and Cohen-Haeupler-Schulman's constructions.

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