(programming required) Write a program, in a language of your choice (but see the warning below), that implements the algorithm in Figure 4.16, and outputs the list of the 212 = 4096 different 23-bit...

(programming required) Write a program, in a language of your choice (but see the warning below), that implements the algorithm in Figure 4.16, and outputs the list of the 212 = 4096 different 23-bit codewords of the Golay code in a file, one per line. The Golay code is named after Marcel Golay, a Swiss researcher who discovered them in 1949, just before Hamming discovered what would later be called the Hamming code. A slight variant of the Golay code was used by NASA around 1980 to communicate with the Voyager spacecraft as they traveled to Saturn and Jupiter. Implementation hint: suppose you represent the set S as an array, appending each element that passes the test in Line 3 to the end of the array. When you add a bitstring x to S, the very next thing you do is to consider adding x + 1 to S. Implementing Line 3 by starting at the x-end of the array will make your code much faster than if you start at the 00000000000000000000000-end of the array. Think about why! Implementation warning: this algorithm is not very efficient! We’re doing 223 iterations, each of which might involve checking the Hamming distance of as many as 212 pairs of strings. On a mildly aging laptop, my Python solution took about ten minutes to complete; if you ignore the implementation hint from the previous paragraph, it took 80 minutes. (I also implemented a solution in C; it took about 10 seconds following the hint, and 100 seconds not following the hint.)