Coding Theory

Fifth Assignment, Cyclic Codes: due Mon. Apr. 16

  1. CT 4.2.21: d.
  2. CT 4.3.4.
  3. CT 4.3.6: a.
  4. CT 4.3.8 (4.3.11 in the old edition).
  5. CT 4.3.9: e (4.3.12: e in the old edition). Find the remainders when each x^i is divided by g.
  6. CT 4.4.6: f,g.
  7. A study of binary cyclic codes of length 14.
    a. Factor x^12+1 .
    b. How many distinct cyclic codes of length 14 are there?
    c. Describe concisely all possible codes by giving for each code: d. What are the possible dimensions? How many codes are there for each dimension?
    e. There are three distinct codes of rate 1/2. For each one find
  8. CT 4.5.5: g; this problem concerns the Golay code.