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Code 3 fails the prefix-free condition because specific codewords act as prefixes for other codewords within the same code. Specifically, the codeword 0 assigned to $x_1$ is a prefix of the codeword 00 assigned to $x_3$, and the codeword 1 assigned to $x_2$ is a prefix of the codeword 11 assigned to $x_4$.

Conditions: Use the Code 3 column of the displayed table.; Apply the prefix-free definition: no codeword is a prefix of another.

Code 3 fails the prefix-free condition because specific codewords act as prefixes for other codewords within the same code. Specifically, the codeword 0 assigned to $x_1$ is a prefix of the codeword 00 assigned to $x_3$, and the codeword 1 assigned to $x_2$ is a prefix of the codeword 11 assigned to $x_4$.

Conditions: Use the Code 3 column of the displayed table.; Apply the prefix-free definition: no codeword is a prefix of another.

A prefix-free code is a code in which no codeword appears as the initial segment (prefix) of any other codeword. For every pair of distinct codewords, neither may begin with the other as a prefix.

Conditions: Defined relative to concatenation of binary strings.; For every pair of distinct codewords $c_a$, $c_b$, neither $c_a$ is a prefix of $c_b$ nor $c_b$ is a prefix of $c_a$.

A prefix-free code is a code in which no codeword appears as the initial segment (prefix) of any other codeword. For every pair of distinct codewords, neither may begin with the other as a prefix.

Conditions: Defined relative to concatenation of binary strings.; For every pair of distinct codewords $c_a$, $c_b$, neither $c_a$ is a prefix of $c_b$ nor $c_b$ is a prefix of $c_a$.