How NASA’s Mariner 9 probe encoded images

NASA set Mariner 9 to photograph Mars in 1971. The images had to be encoded for transmission using an error-correcting code, otherwise they would be significantly corrupted when they were received on Earth. 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. The previous post explained a way to construct Hadamard matrices of order 2n. Use this process to create a 32 × 32 Hadamard matrix H and create a 64 × 32 matrix M by stacking H on top of −H. Then form a matrix M′ by changing all the −1 entries to 0. The rows of M′ are the code words. For a 6-bit photo pixel value, one of the bits determines whether to read a code word from the top half or bottom half of M′. The other five bits determine which row to choose. So a pixel is transmitted as a 32-bit codeword c, one of the 64 rows of M′.…