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GolfScript, 53 bytes

~:a;{{2base}:b~.,8\-[0]*\+}%[]*a,b,/{b.{(a=}""if}%""+

Try it online!

This is my second GolfScript submission, so I might be able to improve it. I haven't decided on the best way to write explanations for these so this time I'll leave a commented version:

~ # Evaluate the input
:a; # Store the encoder alphabet (top of stack) as variable a
{ # Open a block (like anonymous function) to run on each codepoint:
 {2base} # A block which calls `2 base` (convert to/from base 2).
 :b # Assign the block to b
 ~ # and call it on the codepoint.
 ., # Push the length of the binary digit list.
 8\- # Subtract it from 8.
 [0]* # Push a list of that many zeroes.
 \+ # Prepend it to the binary codepoint.
}% # Close this block and call it on each codepoint (map).
[]* # Flatten the list by joining it on nothing.
a, # Push the length of a.
 b # Convert it to binary.
 , # The length of the digit list.
 / # Split the codepoint list into chunks of this size.
{ # Open a block to run on each chunk:
 b. # Convert the chunk from binary to decimal.
 { # A block that takes a 1-based index
 (a= # decrements and indexes into a.
 } # This returns a number, so we have to coerce to string later.
 "" # The empty string.
 if # If the number is zero, return the empty string,
 # and otherwise run the block.
}% # Run this block on each chunk (map).
""+ # Append an empty string to coerce to a string.