21+ hour, 53+ min ago   (287+ words) Error correcting codes are most simply described in terms of the errors they can certainly correct. For example, the Hadamard code used for the Mariner 9 probe to Mars encoded each 6-bit pixel to a 32-bit codeword in such a way…...

22+ hour, 56+ min ago   (469+ words) Hadamard matrices are in the news following the recent announcement of a newly discovered Hadamard matrix. I’ve written three posts on Hadamard matrices recently, one as a sort of introduction and two on applications: the error correcting code used in…...

2+ day, 13+ hour ago   (220+ words) Yesterday Levent Alpöge announced that he and his colleagues had discovered a new Hadamard matrix using Claude AI. That motivated a post I wrote this morning on how to construct Hadamard matrices. I mentioned in that post that these matrices…...

2+ day, 14+ hour ago   (276+ words) The images were encoded for transmission using a code based on Hadamard matrices, specifically a (32, 6, 16) Hadamard code. This means that each 6-bit pixel value was encoded as a 32-bit code word, with all code words differing in at least 16 positions....

2+ day, 23+ hour ago   (507+ words) A Hadamard matrix is an orthogonal matrix whose entires are all either 1 or − 1. For example is a Hadamard matrix of order 2. True to Stigler’s law of eponymy, James Joseph Sylvester investigated Hadamard matrices before Jacques Hadamard. Sylvester saw how to…...

4+ day, 1+ hour ago   (411+ words) Suppose you’ve never worked at the command line and you’re reading a book about the bash shell. You read that!$ is a shortcut to refer to the last word of the previous command. That little fact will almost certainly not…...

5+ day, 27+ min ago   (198+ words) I was reading a blog post on boat names because it was on Hacker News this morning. The post contained a link to a data set on dog names in NYC and I poked around the data a little. The…...

5+ day, 2+ hour ago   (348+ words) Suppose you were able to go back in time, to an era before computers, and give someone contemporary cryptography. Encryption methods that are essentially unbreakable now would certainly be unbreakable then. But there’s a catch: not only do attackers not…...

6+ day, 3+ min ago   (195+ words) The following extraordinary paragraph comes from Knuth’s TAOCP Volume 4A, right before the last set of exercises. Many of the exercises below ask a modern reader to find and/or to correct errors in the literature of bygone days. The point…...

5+ day, 23+ hour ago   (237+ words) In science and engineering classes, you might describe a system using Newton’s laws and end up with a differential equation. You then solve the differential equation, analytically or numerically, to see how the solutions behave. You might also do the…...