## Related questions with answers

Question

Construct a (7, 3) code in which every nonzero codeword has Hamming weight at least 4.

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 2We will construct $(7,3)$ code generated by the standard generator matrix

$G=\begin{pmatrix} 1 & 0 & 0 & 1 & 1 & 0 & 1\\ 0 & 1 & 0 & 1 & 1 & 1 & 0\\ 0 & 0 & 1 & 1 & 0 & 1 & 1 \end{pmatrix}.$

Message words of $(7,3)$ code are:

$\{ 000, \ 001, \ 010, \ 011, \ 100, \ 101, \ 110, \ 111 \} .$

Multiplying message words with $G$ we get appropriate codewords:

$\begin{align*} \{ &0000000, 0011011, 0101110, 1001101, \\ &0110101, 1100011, 1010110, 1111000 \}. \end{align*}$

We see that every nonzero codeword has Hamming weight at least 4.

## Create a free account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy

## Create a free account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy

## Recommended textbook solutions

## More related questions

- computer science

1/4

- computer science

1/7