Turning the diagrams into code was easy but the first exhaustive tests have shown some.... behaviour that I suspected but didn't find at first.

The principle of the popcount is to flip the whole word when not enough bits are set.

0 => 8
1 => 7
2 => 6
3 => 5

OK but what about 4 ? 

Flipping the word when 4 bits are set will not change the number of set bits. So the only effect is to set the corresponding "flip" bit. There are a number of pros & cons about its activation.

• Defaulting to f=0 (no flip) means less activity, spectrum power is lower at high frequencies.
• f=1 would increase activity and potentially reduce droop.
• Since F could be either 1 or 0 without actual effect, it acts like a possible "return to neutral" bit and be occasionally "chosen" to favour a certain parity.
• OTOH 4 is fairly common and if/when the byte is altered, the "nevermind" value of f could reduce the rate of error detection, so it better be fixed in all cases.
• It is easier to just detect > 3 because the MSB is set for 4,5,6,7... and 8 is not representable in 3 bits. So I think that settles the issue.

Unfortunately it's more complex than that.

The code might have some bugs but already shows that

• 4 flips 15 times in 70 occurrences. Fine, no worries, though it could be better.
• 5 flips 20 times out of 56 !

  31 : 00011111 : 5 : 1?0 : -
  47 : 00101111 : 5 : 1?0 : -
  55 : 00110111 : 5 : 1?0 : -
  59 : 00111011 : 5 : 1?0 : -
  79 : 01001111 : 5 : 1?0 : -
  87 : 01010111 : 5 : 1?0 : -
  91 : 01011011 : 5 : 1?0 : -
  103 : 01100111 : 5 : 1?0 : -
  107 : 01101011 : 5 : 1?0 : -
  115 : 01110011 : 5 : 1?0 : -
  143 : 10001111 : 5 : 1?0 : -
  151 : 10010111 : 5 : 1?0 : -
  155 : 10011011 : 5 : 1?0 : -
  167 : 10100111 : 5 : 1?0 : -
  171 : 10101011 : 5 : 1?0 : -
  179 : 10110011 : 5 : 1?0 : -
  199 : 11000111 : 5 : 1?0 : -
  203 : 11001011 : 5 : 1?0 : -
  211 : 11010011 : 5 : 1?0 : -
  227 : 11100011 : 5 : 1?0 : -

  That's ... a problem : this increases the max run length ! The common condition is MSB=11. If the word was not flipped, there would be the solution to combine the LSB and MSB (instead of two LSB) to bound the situation only to cases where a 1 delimits the start and end of the word. But it's not possible.

Apparently a better, precise popcount is required. I didn't know how to do it but it seems I have figured out a solution at last.