The following sequence was generated by a linear feedback shift register. Determine the recurrence that generated it.

1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0,
0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0,
0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1,
1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0,
1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1,
1, 1, 1, 1, 1

(It is stored in the downloadable computer files (bit.ly/2JbcS6p) under the name L101.)

The following are the first 100 terms of an LFSR output. Find the coefficients of the recurrence.

1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0,
0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1,
1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0,
1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1,
0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0,
1, 0, 0, 0, 0

(It is stored in the downloadable computer files (bit.ly/2JbcS6p) under the name L100.)

The following ciphertext was obtained by XORing an LFSR output with the plaintext.

0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0,
1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0,
1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1

Suppose you know the plaintext starts

1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0

Find the plaintext. (The ciphertext is stored in the downloadable computer files (bit.ly/2JbcS6p) under the name L011.)