Traveling outwards from the Earth in plastic bags in a tube, it would survive minutes, 'till the bags heated up in the solar radiation, burst and the whole of the inside of the tube was filled with mixed blood clotts, melted plastic and superheated steam (over 200C - 390 F in direct sunlight), the protein's would denature. No recognisable DNA could survive.
Once you've extracted, dried and frozen your DNA you're going to be faced with two problems:
Thermal and radiation damage is going to be an issue inside the near-to-sun solar system, it gets hot in near Earth space in the sun's light, swings between +200 celsius and -200 celsius (+392 to -328 Fahrenheit) the bake/freeze cycle isn't going to do your precious cargo much good. Meanwhile your coolant is boiling off at an allarming rate. So you'll need shielding against this.
As soon as you're out of the solar system into interstellar then intergalactic space, everything settles down tending towards the temp of the microwave bacground at 2.7 K - so no more gross thermal or radiation damage to worry about - till you get to the other end of the journey. (You're going to need more coolant!)
Even if you cool DNA down, to eliminate de-methylation and de-amination errors via thermal decay, the Atomic Elements that make-up your DNA - well many of them are themselves radioactive to some extent (we're all familiar with Carbon dating - only possible because carbon has radioactive isotopes) - so they damage themselves.
DNA may contain a large number of postmortem mutations, increasing
But Mutation is not the greatest issue, fragmentation is:
The oldest intact (more or less) genome known to exist (on Earth) is 700,000 years old. Anything older than 1.5 Million years is thought to be too fragmented to be able to be readable.
This is compounded and confounded because of the DNA / nDNA issue: Most DNA is Non-Coding, the mixture reaches a threshold when it's all just a nucleotide soup without coherence.
Thanks to Yisela on biology SE
Digital encoding of microchips isn't going to last more than a couple of decades, quantum mechanical effects mean that anything on only slightly above the atomic level won't last a very long time.
If the DNA code were transcribed onto gold sheets, then no degredation would occvr*, and your "samples* would last indefinitley. The book for each person would be sizeable - there are 6,469.66 Million base pairs (each pair being two of Adenine, Thymine, Guanine and Cytosine) That's more than a few library shelves worth of books, or even libraries worth. The print would need to be fine, and the sheets, thin - this would be a trade-off between weight and fragility. There are bespoke laser-etched "Saphire" disks proposed, but none in mass production yet, they may offer a marginaly better solution. (Beware - They're asking for funding on the site.)
*not quite true, it's always a trade-off size versus: quantum mechanical effects occur which make atoms wander over time. The bigger your writing on the gold sheets, the slower that they'll be noticable - a few tens of billion years enough for you if you write large?
Found by members of your species with a knowledge of the standard DNA notations used, this would be interpretable. Aliens are a different pobal of Soobishes.
- The Anodised Aluminium plates that Nasa sent out with The Pioneer spacecraft in case of alien interception were basic:
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It gave pictures of us and Earth's position relative to pulsars, but we got it significantly wrong, the frequency of pulsars was not correct by modern standards which may make the coordinates uninterpretable.
The theory of communicating with aliens is complex and fraught with confounding issues, not the least of which is that we haven't met any (knowingly).
We simply don't know if we even could communicate with aliens sufficiently well to make them get what we're trying to say, or if they'd care enough to try and reproduce our species anyhow.
Without a more sophisticated response, and a considerably greater effort, the human race is over.