Show that the codeword a cannot be a valid codeword.

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  • Thread starter Reyawakens
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In summary, a valid codeword is a sequence of symbols or characters that meets the criteria set by a coding system, while an invalid codeword does not meet these requirements. To show that a codeword is not valid, it can be compared to the rules of the system or proven mathematically. Proving a codeword is not valid is significant for maintaining the accuracy and integrity of the system and preventing errors. A codeword can be considered valid in some cases but not others, depending on the coding system and context in which it is used.
  • #1
Reyawakens
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Let d=d1d2d3d4d5d6d7 be a valid codeword of Hamming (7,4) code. Suppose a=a1a2a3a4a5a6a7 be another codeword that differs from d precisely at two bits. Show that the codeword a cannot be a valid codeword.

May I ask how to solve this type of problem?
 
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  • #2
what's the Hamming distance of the (7,4) code? (hint: it's 3)

Can a valid codeword exist at a Hamming distance of 2 bits in a code with a Hamming distance of 3?
 

1. Why is it important to show that a codeword cannot be a valid codeword?

It is important to show that a codeword cannot be a valid codeword because it ensures the accuracy and reliability of the data being transmitted. If an invalid codeword is used, it can result in errors and corruption of the data.

2. What does it mean for a codeword to be "valid"?

A valid codeword is a sequence of symbols or characters that can be accurately transmitted and decoded without any errors. It follows the rules and guidelines set by the coding system in place.

3. How can you determine if a codeword is not valid?

A codeword can be determined as not valid if it does not follow the specific coding rules and guidelines, such as having the correct number of symbols or characters, or if it contains errors or inconsistencies.

4. What are some possible reasons for a codeword to be invalid?

There are several reasons why a codeword may be invalid, such as errors in transmission, incorrect coding or decoding, or the use of an outdated or incorrect coding system.

5. Can an invalid codeword be fixed or corrected?

In some cases, an invalid codeword can be fixed or corrected by identifying and correcting the errors or inconsistencies. However, in other cases, a new codeword may need to be generated to ensure accuracy and reliability of the transmitted data.

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