Recall that F = F_ 3[x]/ is a finite field of order 3^ 2. Find a primitive eleme
ID: 1721519 • Letter: R
Question
Recall that F = F_ 3[x]/ is a finite field of order 3^ 2. Find a primitive element and write out the cyclotomic cosets along with their minimal polynomials. Use F to construct a BCH code C of length n = 8 and design distance 5. Give a generator polynomial and generator matrix for C. What is the dimension of C? Give a check polynomial for C and find a parity check matrix H. What is the minimum distance of C Justify your answer. How many errors can C correct in any codeword? Is C a perfect code? If so, prove it. If not, give an example of a received vector which C cannot correct.Explanation / Answer
a.F=F3|X|/<X2+1> is the order of 32
the premitive element is 9/10
there f3 of the 9/10.
b.the diemension of C is bidirectionaland rectangular
c.when the diemension of C rectangular is the polynomial and the parity check of matrix H is height
d. the minimum distence of C apprximately 7.8 there are some errors ignore that and calculate that
c.yes, the above given code is right because the length and distance are also for construct of F.