In the following questions, wherever required, use the Galois fields F23={0,1,α,α2,α3=1+α,α4=α+α2,α5=1+α+α2,α6=1+α2}andF24={0,1,α,α2,α3,α4=1+α,α5=α+α2,α6=α2+α3,α7=1+α+α3,α8=1+α2,α9=α+α3,α10=1+α+α2,α11=α+α2+α3,α12=1+α+α2+α3,α13=1+α2+α3,α14=1+α3}. 1. Which one of the following cannot be a binary primitive BCH code of the length?
4. In BCH code, suppose the generator polynomial g(X) has 2t+1 number of non-zero coefficients, then g(X) is the codeword polynomial of the codeword with the weight equal to dmin.
6. Consider the same example which we discussed in the theory of this experiment (Example 3).For the (15,5,7) triple-error-correcting BCH code, suppose that v=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] is transmitted, and the vector r=[0,0,0,1,0,1,0,0,0,0,0,0,1,0,0] is received. Then r(X)=X3+X5+X12. Assume that we have performed Berlekamp's iterative algorithm up to the 3rd iteration (i.e, μ=3) and is provided in the Table 6.
