[melaniejs (OP)]

Paul asks:

Is there sufficient space in a barcode or Q code to store one's DNA?

Anyone here knows?

[Bored chemist]

No.
Each cell contains roughly 1.5GBytes
A QR code is about 3K so that's half a million or so QR codes for each cell.

[alancalverd]

Or yes, if you look at it differently.

 A 13-digit linear barcode can uniquely identify anyone who has ever lived, and each person's DNA is unique (apart from a few clones). So if you have mapped and filed a person's DNA against a barcode database, you can retrieve the entire sequence.

[Bored chemist]

Well...
You can put that database into some sort of order. Say time of birth.
Then you can adopt a standard record length for each entry- pad it with leading zeroes if you need to.
And into the "data " field, you put a copy of the DNA sequence.  You can code the 4 bases as 00 01 10 and 11

You now have a list of about 10 billion very long numbers.
And you can concatenate the whole lot to form one enormously long binary number.

And you can put a binary point (like a decimal point) in front of it to turn it into the binary representation of a fraction.

Then, you can take the bar code from a tin of beans or something and fold it so that teh length is divided in proportion to that fraction.

That lets you put everybody's DNA on one bar code.

Good luck reading it to a high enough precision.

[hamdani yusuf]

Or yes, if you look at it differently.

 A 13-digit linear barcode can uniquely identify anyone who has ever lived, and each person's DNA is unique (apart from a few clones). So if you have mapped and filed a person's DNA against a barcode database, you can retrieve the entire sequence.

The database itself can be compressed due to the similarities in human DNA.

While the genetic difference between individual humans today is minuscule – about 0.1%, on average – study of the same aspects of the chimpanzee genome indicates a difference of about 1.2%. The bonobo (Pan paniscus), which is the close cousin of chimpanzees (Pan troglodytes), differs from humans to the same degree. The DNA difference with gorillas, another of the African apes, is about 1.6%. Most importantly, chimpanzees, bonobos, and humans all show this same amount of difference from gorillas. A difference of 3.1% distinguishes us and the African apes from the Asian great ape, the orangutan. How do the monkeys stack up?  All of the great apes and humans differ from rhesus monkeys, for example, by about 7% in their DNA.

http://humanorigins.si.edu/evidence/genetics