Suppose that C is a linear code with Hamming weight 3 and that C'is one with Hamming weight 4. What can C' do that C can’t?
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Suppose that C is a linear code with Hamming weight 3 and that C'
is one with Hamming weight 4. What can C' do that C can’t?
Step by step
Solved in 2 steps
- Let C be a binary linear code. Show that either every member of Chas even weight or exactly half the members of C have even weight.Let C be an (n, k) linear code. For each i with 1 ≤ i ≤ n, let Ci ={v ∈ C | the ith component of v is 0}. Show that Ci is a subcode of C.Let A={+,x,a,b}. Show that (a*V ba)+ b is regular over A.
- Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + 1 and g(x) = x ^2. The composition of fog (-2) is --Show that StartFraction d Over dx EndFraction (ln kx)equalsStartFraction d Over dx EndFraction ln x, given that xgreater than 0 and kgreater than 0 is a real number.Show that in a binary linear code, either all the code words end with0, or exactly half end with 0. What about the other components?
- Prove that a linear code C of minimum distance dmin can correct up to t errors if and only if dmin dmin 2t + 1. Briefly explain BCH codes and its properties.Is A a subset of B if; A = {5,2,1} B ={ 6, 1, 2Let Ci and C2 denote two cyclic codes with the same block length n, with generator polynomials gi(X) and g2(X), and with minimum distances dı and d2, respectively. Define Cmax = C1 UC2 and Cmin = C1 nC2. 1. Is Cmax a cyclic code? Why? If yes, what is its generator polynomial and its minimum distance? 2. Is Cmin a cyclic code? Why? If yes, find its generator polynomial. What can you say about its minimum distance?
- Let C be a non-zero cyclic code in Rn. If g(x) is the monic polynomial of minimum degree in C, prove that C is generated by g(x)Computer Science Use the pumping lemma to check if the following languages are "regular" or "not regular". Show your complete solution.L = { w ε {0,1}* :w = 0*(10*)* }Let E : y2 = x3 + 3x + 4 be an elliptic curve over F37. (a) Find all the elements of the elliptice curve group.(b) Find the order of the group.(c) Find a primitive element of this group and call it G.(d) Compute [30]G = G ⊕ G ⊕ · · · ⊕ G (addition of 30 many G’s) kindly help with full explanation. Thank you!