With[{n=582285,s=2,k=2},
  Flatten[MapIndexed[{1,-1} #2+{0,
              k}->{1,1,2} Mod[Quotient[#1,{2 k,2,1}],{s,k,2}]+{1,0,-1}&,
      Partition[IntegerDigits[n,2 s k,s k],k],{2}]]]