A note on variable-length codes with constant hamming weights

A recent paper described a variable-length integer code based on the Goldbach conjecture where every codeword had exactly 2 1-bits but with an extremely irregular structure. A later,unpublished,work produced a much more regular code,again with a Hamming weight of 2. This paper extends that later work to weight-3 and weight-4 codes,which are shown to be competitive with more-usual codes over a useful range of values.