HammingDistance.h

typedef void (*HammingDistanceCallback)(uint8_t* Buf);

template <size_t NumBytes, size_t Distance>
static void HammingDistanceRecurse(uint8_t Buf[NumBytes], HammingDistanceCallback Callback, int Level, int StartPosition)
{
    Callback(Buf);

    if (Level == Distance)
        return;

    int i;
    for (i=StartPosition; i<8*NumBytes; i++)
    {
        Buf[i/8] ^= 1 << (i%8);
        HammingDistanceRecurse<NumBytes, Distance>(Buf, Callback, Level+1, i);
        Buf[i/8] ^= 1 << (i%8);
    }
}

template <size_t NumBytes, size_t Distance>
void HammingDistance(uint8_t Buf[NumBytes], HammingDistanceCallback Callback)
{
    return HammingDistanceRecurse<NumBytes, Distance>(Buf, Callback, 0, 0);
}

test_HammingDistance.cpp

#include <stdint.h>
#include <stddef.h>
#include <stdio.h>
#include "HammingDistance.h"

void Callback(uint8_t Buf[])
{
    int i;

    for (i=0; i<16; i++)
        printf("%02x ", Buf[i]);

    printf("\n");
}

int main()
{
    uint8_t Zeroes[16] = {0};

    // Loop over all strings with hamming distance <= 2 from zeroes.
    HammingDistance<sizeof(Zeroes), 2>(Zeroes, &Callback);

    return 0;
}