You translation is good.

Here are a few suggestions for your translation: “all bit symbol series” = “bit-strings”

“connected” = “related”.

There is a mistake. The word “antisymmetric” must surely be “symmetric”.

As described the relation is an equivalence relation; it is reflexive, symmetric, and transitive.

Any time we have a “same as” relation that is true.

If a=10100001000 & b=10111111111 then clearly aRb & bRa but a is not equal to b.

Therefore the relation is not antisymmetric.