#!/usr/bin/env python3
import numpy as np
from functools import lru_cache

@lru_cache(100)
def radix_matrix(shape):
    return (2 ** np.arange(shape[0] * shape[1])).reshape(shape)

def binmtx2key(arr):
    weights = radix_matrix(arr.shape)
    return ((weights * arr).sum(),) + arr.shape

def key2binmtx(key):
    shape = key[1:]
    width = shape[0] * shape[1]
    binstr = bin(key[0])[2:].rjust(width, '0')
    return (np.array(binstr, dtype='c') == b'1').reshape(shape) + 0

k = np.array([[1, 1], [1, 0]])
kencoded = binmtx2key(k)
print(kencoded)
print(key2binmtx(kencoded))