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Homework 2

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Reading:

  • Section 4.1 (but light on the bound stuff), 4.2, 4.3, 4.5, 4.6.
  • Then section 4.1 again.


Problems:

  1. Problems 4.1, 4.2, 4.3, 4.4, 4.5, 4.6,
  2. 4.8(a) Also find the generator matrix for this code.
  3. 4.11, 4.12, 4.13, 4.14, 4.15, 4.16(a,b)
  4. The generator matrix for a code over $GF(2)$ is given by

    \begin{displaymath}G = \left[\begin{array}{cccccc}
1&0&1&0&1&1 \\
0&1&1&1&0&1 \\
0&1&1&0&1&0
\end{array}\right]
\end{displaymath}
      1. Find the generator matrix and parity-check matrix for an equivalent systematic code.
      2. List the vectors in the orthogonal complement of the code.
      3. Form the standard array for this code.
      4. How many codewords are there of weight $0,1,\ldots,6$ ?
      5. Find the codeword with 101 as information symbols.
      6. Decode the received word 111001.
  5. Given a code with a parity-check matrix $H$ , show that the coset with syndrome $\sbf$ contains a vector of weight $w$ if and only if some linear combination of $w$ columns of $H$ equals $\sbf$ .

 

Copyright 2008, Todd Moon. Cite/attribute Resource . admin. (2006, June 21). Homework 2. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Error_Control_Coding/hw2new.html. This work is licensed under a Creative Commons License Creative Commons License