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Introduction:
In coding theory, error correction is a technique used to detect and correct errors in transmitted data. The maximum number of errors that can be corrected by a code is determined by its error-correcting capability. In this case, we have a code with four valid codewords: 00000000, 11001100, 00110011, and 11111111. We need to determine the maximum number of errors that can be corrected for this code.

Error-Correcting Capability:
The error-correcting capability of a code is determined by the minimum Hamming distance between its codewords. The Hamming distance is the number of bit positions at which two codewords differ. The larger the minimum Hamming distance, the better the error-correcting capability of the code.

Calculating Hamming Distance:
To calculate the Hamming distance between two codewords, we compare them bit by bit and count the number of differences. Let's calculate the Hamming distances between the given codewords.

Hamming distance between 00000000 and 11001100 = 4
Hamming distance between 00000000 and 00110011 = 4
Hamming distance between 00000000 and 11111111 = 8
Hamming distance between 11001100 and 00110011 = 4
Hamming distance between 11001100 and 11111111 = 4
Hamming distance between 00110011 and 11111111 = 8

Minimum Hamming Distance:
The minimum Hamming distance is the smallest Hamming distance among all pairs of codewords. In this case, the minimum Hamming distance is 4, which is the distance between 00000000 and 11001100. Therefore, the error-correcting capability of this code is 4-1 = 3, where 1 is subtracted because the code can only correct errors up to the floor of (minimum Hamming distance - 1) / 2.

Conclusion:
In conclusion, the maximum number of errors that can be corrected for the given code is 1. This means that if there is an error in one bit of a received codeword, it can be corrected to the nearest valid codeword. However, if there are two or more errors, the code may not be able to correct them and may produce an incorrect output. Therefore, it is important to choose a code with a higher error-correcting capability if the transmission channel is prone to multiple errors.