$ jq -n -c -f rep-string.jq
 {"1001110011":[[2,"10011"]]}
 {"1110111011":[[2,"1110"]]}
 {"0010010010":[[3,"001"]]}
 {"1010101010":[[5,"10"],[2,"1010"]]}
 {"1111111111":[[10,"1"],[5,"11"],[3,"111"],[2,"1111"],[2,"11111"]]}
 {"0100101101":[]}
 {"0100100":[[2,"010"]]}
 {"101":[]}
 {"11":[[2,"1"]]}
 {"00":[[2,"0"]]}
 {"1":[]}