We derive a simple algorithm for the ranking of binary sequences of length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> and weight <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">w</tex> . This algorithm is then used for source encoding a memoryless binary source that generates O's with probability <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</tex> and l's with probability <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p = 1 - q</tex> .
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J. Schalkwijk (1972) studied this question.
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