Hamming space
Hamming space is like a game of spot the difference between two pictures. Imagine you have a picture of a dog and a picture of a cat, and you want to find out how different they are. You can look at each pixel in the pictures and see if they have the same color or not. If they are different, you make a mark on a piece of paper. When you finish comparing all the pixels, you count up the marks to see how many differences there are.
Now, let's say you have two words like "cat" and "bat." You want to know how different they are, but you can't just look at each letter by itself. Instead, you compare the letters in the same positions in both words. In this case, the first letter is "c" in "cat" and "b" in "bat." Those letters are different, so you make a mark. Then you compare the second letter, which is "a" in both words, so you don't make a mark. Finally, you compare the third letter, which is "t" in "cat" and "t" in "bat." Those letters are the same, so you don't make a mark.
Overall, there is only one difference between "cat" and "bat" - the first letter. When you count up the differences between two words in this way, you are creating a Hamming space. It's like a special way of measuring how different two things are by looking at the differences between their parts.
Now, let's say you have two words like "cat" and "bat." You want to know how different they are, but you can't just look at each letter by itself. Instead, you compare the letters in the same positions in both words. In this case, the first letter is "c" in "cat" and "b" in "bat." Those letters are different, so you make a mark. Then you compare the second letter, which is "a" in both words, so you don't make a mark. Finally, you compare the third letter, which is "t" in "cat" and "t" in "bat." Those letters are the same, so you don't make a mark.
Overall, there is only one difference between "cat" and "bat" - the first letter. When you count up the differences between two words in this way, you are creating a Hamming space. It's like a special way of measuring how different two things are by looking at the differences between their parts.