This is my first question here, so if I am doing things incorrectly, please let me know. Now on to the question:


The forcing notion $Fn(\kappa,2)$, which constists of partial functions from $\kappa$ to $2$ with finite support, ordered by reverse inclusion, is known to add $\kappa$ new cohen reals.


Are there similare forcing notions adding $\kappa$ new random, sacks, prikry, or Mathias reals?



Are there forcing notions adding $\kappa$ random, sacks, prikry, or Mathias reals?
The reason $Fn(\kappa,2)$ works for adding $\kappa$ new cohen reals is, because there exists a bijection between $\kappa$ and $\kappa\times\omega$, therefore the forcing $Fn(\kappa,2)$ is isomorphic (as a partial order) to $Fn(\kappa\times\omega,2)$ which itself is isomorphic to a Finite Support iteration of Length $\kappa$ of Cohen Forcing.


Similarly, for any forcing of your desired type (be it random, sacks, ... forcing), you could use a Finite Support iteration of length $\kappa$ to obtain your desired forcing. If you need an introduction to Forcing Iterations, Jechs book on Set Theory is a good start.


