📝 Cyclic Code Encoder Using Polynomials

Q1. If a transmitted codeword is divided by the generator polynomial \(g(x)=x^3+x+1\) and the remainder is non‑zero, what can be inferred about the received word?

💡 Difficulty: easy | ✅ Correct: C

Q2. Two cyclic encoders use generator polynomials \(g_a(x)=x^3+x^2+1\) and \(g_b(x)=x^3+x+1\). For the same 5‑bit message, which encoder tends to produce codewords with higher average Hamming weight?

💡 Difficulty: medium | ✅ Correct: A

Q3. Compare the error‑detecting capability of generator polynomials \(g_1(x)=x^4+x+1\) and \(g_2(x)=x^4+x^3+1\) for a 7‑bit message. Which statement is true?

💡 Difficulty: easy | ✅ Correct: A