#!/usr/bin/python3

import itertools
import random
import functools
import operator


def polynomial_value(polynomial, x):
    return functools.reduce(operator.xor, [polynomial[monomial] * functools.reduce(operator.mul, [x[i] for i in monomial], 1) for monomial in polynomial], 0)


def generate_test(r, m):
    random_polynomial = dict((multi_index, round(random.uniform(0, 1))) for l in range(r + 1) for multi_index in itertools.combinations(range(m), l))
    correct_word = [polynomial_value(random_polynomial, x[::-1]) for x in itertools.product(*[[0, 1]] * m)]
    corrupted_word = correct_word[:]
    for _ in range((2 ** (m - r - 1)) - 1):
        corrupted_word[round(random.uniform(0, len(correct_word) - 1))] ^= 1
    return corrupted_word, correct_word


if __name__ == "__main__":
    print(generate_test(2, 4))