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arXiv · 1202.2794

Query Matrices for Retrieving Binary Vectors Based on the Hamming Distance Oracle

Vinay Anant Vaishampayan
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Abstract

The Hamming oracle returns the Hamming distance between an unknown binary $n$-vector $x$ and a binary query $n$-vector y. The objective is to determine $x$ uniquely using a sequence of $m$ queries. What are the minimum number of queries required in the worst case? We consider the query ratio $m/n$ to be our figure of merit and derive upper bounds on the query ratio by explicitly constructing $(m,n)$ query matrices. We show that our recursive and algebraic construction results in query ratios arbitrarily close to zero. Our construction is based on codes of constant weight. A decoding algorithm for recovering the unknown binary vector is also described.

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Vinay Anant Vaishampayan. 2012-02-13. Query Matrices for Retrieving Binary Vectors Based on the Hamming Distance Oracle. https://arxiv.org/abs/1202.2794

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