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.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.