EDIT: I read this question too fast, and misunderstood it. For the correct answer, please see the comments below.
This is a very specialized structure. When "by X" means "X is the method", we don't use articles.
I wrote this by hand=I used a pen instead of typing.
I sent the letter by mail= I used a mail service instead of the internet.
I went there by bicycle=I rode my bicycle there.
NOTE: there is a fairly small number of places where we typically use this pattern. Only use examples that you've seen other people use. It's technically OK to say "I kicked the ball by foot", but we would be much, much, much more likely to use "I kicked the ball with my foot."