Prescribed positive word lengths admit a decipherable code if and only if they admit a prefix code. Counting length- concatenations of words proves the Kraft inequality for any decipherable code; choosing free vertices of the ordered -ary tree constructs a prefix code whenever this inequality holds. Each prefix code has unique decodability.

Ancestors (9)

  1. Kraft inequality
  2. Prefix code
  3. Decipherable code
  4. Unique decodability
  5. Coding theory
  6. Algebra
  7. Area of mathematics
  8. Mathematics
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