What the name for binary code where each integer number represented by equal number of 1s and 0s

Question

I wondering if there is a specific name for binary encoding of integer when each representation has the same number of 1s and 0s. Here an example

I believe this kind of code should be in frequent used in artificial binary networks to equalize number of active neurons for any input. I thought this kind of code is related to Hamming code, but it seems I was wrong.

These numbers have the same "Hamming weight" or "population count". — m69's been on strike for years, Mar 23 '17 at 19:34
Here's a related answer: https://stackoverflow.com/questions/36451090/permutations-of-binary-number-by-swapping-two-bits-not-lexicographically/36466454#36466454 — m69's been on strike for years, Mar 23 '17 at 20:28

score 0 · Answer 1 · answered Mar 24 '17 at 21:55

Thanks a lot to @m69, I got good idea of walking bit algorithm, which after some small modifications does the job. I post this python code here just in case someone else will need it.

def equalcodegen(size):
    x = [ 1 for _ in xrange(size/2)]+[ 0 for _ in xrange(size/2)]
    def walk(seq):
        idx=0
        while seq[idx] != 0: idx+=1
        if idx == 0: 
            s = seq[:]
            yield []
        else:
            seq[idx-1] = 0
            for pos in xrange(idx, len(seq)):
                s = seq[:]
                s[pos] = 1
                yield s
                for p in walk(s[:pos]):
                    if len(p) == 0: continue
                    k = p+s[pos:]
                    yield k


    wset =  [x]+[ x for x in walk(x) ]
    return [ "".join( "%d"%x for x in p) for p in wset ]

if __name__ =="__main__":
    s =  equalcodegen(6)
    for x in s:
        print x

Result:

What the name for binary code where each integer number represented by equal number of 1s and 0s

1 Answers1