We need to form a 4-letter code using the first 10 letters of the English alphabet, where no letter is repeated. This problem is similar to filling vacant places as described in the multiplication principle.

There are 4 vacant places to be filled. The first place can be filled by any of the 10 letters in 10 different ways. Since repetition is not allowed, the second place can be filled by any of the remaining 9 letters in 9 ways. The third place can be filled in 8 ways, and the fourth place can be filled in 7 ways.

Calculation: By the multiplication principle, the total number of codes is the product of the number of ways for each place. Total codes = $10 \times 9 \times 8 \times 7$ Total codes = 5040