Nullspace encoding example

brute_force.cpp

#include <stdio.h>
#include <stdlib.h>  // rand()
#include <string.h>  // strlen()


const char* txt = "THESEMUSTBEUPPERCASELETTERS";
const int colors = 256;

int num (char letter) {
    return (int)letter - 64;
}

int main () {
    int n = strlen(txt);

    // Convert the string to an array of ints, with a large negative
    // int at the end such that the sum over the array is zero.
    int w = n+1;  // width of matrix
    int soln[w];  // vector to encode
    {
        int accum = 0;
        for (int j = 0; j < n; j++) {
            accum += (soln[j] = num(txt[j]));
        }
        soln[w-1] = -accum;
    }

    int i = 0;  // row label

    // We need at least w-1 rows for the null vector to be
    // well-defined.
    while (i < w-1) {
        int res = 0;  // scalar result of row*soln

        int row[w];
        // Populate the row with random elements.
        for (int j = 0; j < w; j++) {
            row[j] = rand()%colors;
            res += row[j]*soln[j];
        }

        // If nullity holds then print.
        if (res == 0) {
            for (int j = 0; j < w; j++) {
                printf("%d", row[j]);

                if (j != w-1)
                    printf("\t");
            }

            printf("\n");
            i++;
        }
    }
}