The function of ' comma + participle' modifier

[JiawenW854]

1. Is 'comma+past participle' structure Adj. modifier or Adv. modifier?
Eg: As a child Frank invented his own secret code,based on rebus-like puzzles and on the substitution of numbers for letters.
In this sentence, does ",based on rebus-like puzzles and on the substitution of numbers for letters'' modify the preceding words "secret code' or the preceding sentence "As a child Frank invented his own secret code"?

2. Does 'comma+present participle' act as Adv. modifier for one hundred percent?

Thank you

[Sage Pearce-Higgins]

There's some controversy on this point. I've heard these participle modifiers described at times as either noun and adverbial modifiers by different (reputable) GMAT teachers. My advice would be not to worry about this distinction too much: in the context of GMAT problems, you're looking for obvious mistakes and GMAT tends to avoid controversial examples.

For example: 'Stacey walked along the street, singing a tune.' Does singing modify Stacey (a noun modifier), or does it modify the verb / clause (an adverbial modifier)? After all, it's Stacey who was singing, but it's also a description of how she walked. What's important to note is that the sentence is fine, because there's a connection between the two actions (they happened at the same time).

What's not fine is this example: 'Stacey walked along the street, living in New York for years.' There's no logical connection between the actions; most people can feel that this sentence doesn't work. Using a 'who' modifier would be better here.

As for your example, I'd be inclined to say that it would work fine without the comma, as that would make clear that it's the code that's based on rebus-like puzzles etc. However, here are two other variants which I think work:

As a child Frank invented his own secret code, which was based on rebus-like puzzles and on the substitution of numbers for letters.
As a child Frank invented his own secret code, basing it on rebus-like puzzles and on the substitution of numbers for letters.