Combinatorics › Counting principles › Bits and binary trees

Locating a single bit error

High school · ●●○○○ 20 pts

A binary code x1x2…x7x_1x_2\ldots x_7 satisfies the parity check equations x4⊕x5⊕x6⊕x7=0x_4\oplus x_5\oplus x_6\oplus x_7=0, x2⊕x3⊕x6⊕x7=0x_2\oplus x_3\oplus x_6\oplus x_7=0 and x1⊕x3⊕x5⊕x7=0x_1\oplus x_3\oplus x_5\oplus x_7=0, where ⊕\oplus is addition modulo 2. A code of this type was changed to 11011011101101 after a bit error occurred at only one position kk during communication, so the bit at position kk flipped. Find kk.

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