The textbook Coding Theory: A First Course by San Ling and Chaoping Xing, published by Cambridge University Press
For example, in the construction of Reed-Solomon codes, the evaluation of polynomials at distinct elements seems straightforward. Yet, the nuances of the Berlekamp-Massey algorithm are subtle. Consulting the solution manual to find an error locator polynomial is only useful if the student works backward from that solution to reconstruct the logic themselves. It is the difference between being a passenger in a car and driving the car yourself; the solution manual should be the GPS, not the steering wheel. solution manual for coding theory san ling
| Chapter | Problem | Topic | Difficulty | | :--- | :--- | :--- | :--- | | 3 | 3.12 | Prove that a binary Hamming code is perfect. | Medium | | 4 | 4.8 | Find all cyclic codes of length 7 over GF(2) and their generator polynomials. | Medium-Hard | | 5 | 5.15 | Decode the received vector (0,1,0,1,0,0,1,1,0,1) using the BCH decoder. | Hard | | 6 | 6.5 | Show that Reed-Solomon codes are MDS. | Hard | | 7 | 7.3 | Implement the Berlekamp-Massey algorithm for a given sequence. | Very Hard | The textbook Coding Theory: A First Course by
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If you are studying coding theory and cannot access the official manual, consider:
Let $I = i : x_i \neq z_i$, $J = i : x_i \neq y_i$, and $K = i : y_i \neq z_i$. Note that $I \subseteq J \cup K$.