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.