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You should a little more time reading about it. Among other features, transactions are described by what is essentially a mini scripting language

> shouldn't be possible

It is restricted by the standard Bitcoin client implementation. Neither the transaction scripting language[0] nor the transaction[1] restricts it, so you would need to do it yourself or write a custom client to embed a message.

[0] https://en.bitcoin.it/wiki/Script

[1] https://en.bitcoin.it/wiki/Transaction#Output

There is all sort of graffiti and other garbage embedded in the blockchain.

http://garzikrants.blogspot.com/2013/04/on-bitcoin-data-spam...