Quantum complexity theory | Computational complexity theory
In communication complexity, the gap-Hamming problem asks, if Alice and Bob are each given a (potentially different) string, what is the minimal number of bits that they need to exchange in order for Alice to approximately compute the Hamming distance between their strings. The solution to the problem roughly states that, if Alice and Bob are each given a string, then any communication protocol used to compute the Hamming distance between their strings does (asymptotically) no better than Bob sending his whole string to Alice. More specifically, if Alice and Bob are each given -bit strings, there exists no communication protocol that lets Alice compute the hamming distance between their strings to within using less than bits. The gap-Hamming problem has applications to proving lower bounds for many streaming algorithms, including moment frequency estimation and entropy estimation. (Wikipedia).
How to detect and correct an error using the Hamming Code. Hamming codes are a type of linear code, see link for intro to linear code: https://www.youtube.com/watch?v=oYONDEX2sh8 Questions? Feel free to post them in the comments and I'll do my best to answer!
From playlist Cryptography and Coding Theory
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From playlist Math for Liberal Studies Lectures
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From playlist Summer of Math Exposition Youtube Videos
In this video I briefly explain what minimum distance is and why it is helpful. Then I explain how to find it "the long way" and the "shortcut." Also during the process, I explain what Hamming Weight and Distance are and how to find them. Codewords from Generating Matrix Video: https://w
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From playlist skill 8 attempt 1
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From playlist MIT 6.451 Principles of Digital Communication II
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