How Hamming codes work

datagenetics.com

145 points·squeakynick··10 comments

Just so you know, this is the same Hamming that published the classic essay, "You and Your Research" (1986): https://www.site.uottawa.ca/~yymao/misc/Hamming_kaiser.html

He's also the mathematician who worked on the Manhattan Project and was asked to confirm the calculations that setting off the first test blast would not create a fireball that would burn up all the oxygen on the planet!

Haha. That's addressed in his essay!!

Is it from him we get hamming and Manhattan distances?

https://en.wikipedia.org/wiki/Richard_Hamming - "Known for: Hamming code, Hamming window, Hamming numbers, Hamming distance, Association for Computing Machinery"

I do not know the origin of the term "Manhattan distance". https://en.wikipedia.org/wiki/Taxicab_geometry says the concept comes from Minkowski in the 1800s, and a Google Scholar and Google ngram search suggest the term originates from around 1960, and the more common older term was "rectilinear distance".

(See https://books.google.com/ngrams/graph?content=Manhattan+dist... .)

Manhattan distance is because Manhattan is a grid, and that's how taxis drive or how people walk.

Yes. That's also described in the link I gave, including a picture.

My question is, who introduced the term to the literature? Was it Hamming, or someone else?

I believe he's also the same hamming who is named for the Hamming Weight: https://en.wikipedia.org/wiki/Hamming_weight

I made a crazy efficient engine for approving prior authorization data using it :D

The same idea can be applied to a two-dimensional grid of bits: http://datagenetics.com/blog/december12014/index.html

I wish someone would make a guide like this for raptor codes.

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