DNA is not just a simple strand of letters (aka nucleotides).
@Hill nice post is correct.
I taught human genetics to med students a looong time ago and this kind of question was almost always asked.
There is some things that would answer your question as "Probably not - ", for ethical reasons and I believe partly due to misunderstanding. Let's look at aneuploidy - to get there we have to talk about ploidy.
Let's limit the discussion using just mammals or plants. The term for these organisms is "eucaryotic" which means they made of cells withe a nucleus, mitochondria, etc. This means we exclude bacteria.
We're going to use lowercase n to represent the number of sets of chromosomes
1n= haploid
2n= diploid
3n= triploid
.... keeps going
Examples: Using Eucaryotic plants and animals
Wheat has been bred into using more and more chromosome sets: 2n, 4n, and 6n
Modern wheat (Triticum ) is derived from ancestors It is: 6n 42 chromosomes. Hexaploid. Einkorn is diploid., 2n and is another kind of wheat.
Strawberries are bred from 2n -> 8n. 8n berries are much larger than 2n berries, 2n wheat grains are smaller and tougher chewing than 6n wheat
Ferns often have an n with hundreds of chromosomes in a set. Example:
One homosporous fern, Ophioglossum reticulatum, has more than 1400 chromosomes – the highest number for any plant, animal, or fungus. For comparison, humans have just 46 chromosomes, grouped into 23 pairs
But! We humans have a wrinkle:
Sex chromosomes.
In birds, females are the heterogametic sex, carrying one copy each of the Z and W sex chromosomes (ZW). Males are homogametic (ZZ).
For humans sex chromosomes are designated X and Y. Male cells are one X chromosome and one Y (XY) , females are XX.
Y chromosomes do not undergo crossing over.
Crossing over --
https://www.genome.gov/genetics-glossary/Crossing-Over
The human genome contains ~3 billion nucleotide pairs, even though most human cells contain 6 billion nucleotide pairs. DNA is a double helix: Each nucleotide on a strand of DNA has a complementary nucleotide on the other strand.
Aneuploidy is chromosome count is wrong or there is a damaged chromosome, from reordering base pairs or loss or gain base pairs.
Examples for aneuploid human babies:
Cri du Chat syndrome is pretty awful, for example. It is caused by a damaged chromosome #5.
https://www.ncbi.nlm.nih.gov/books/NBK482460/
Turners Syndrome is loss of or damage to an X chromosome. Loss of
The point I'm making is that there are vast complexities, and lots of ethical reasons not to do what you ask. Reordering will create aneuploidy -- As you specify "reorder" which is the same as damaging a chromosome.