Find the convolutional code for the message 11011. The convolutional encoder is given in
Fig. 1.
To calculate the convolutional code for the message `11011`, we need to use the specific convolutional encoder you're referring to (which is _______ __________ ____ ____ ___.
________ _____ ________ _________ ________ _________ _________ ______ _______ ___ _____.
__________ ____ ____ _____ __________ ________ ___ ______ ______.
_____ __________ __________ _____ __________ ________ ___.
___ ________ __________ _____ ___ ____ ____ ________ _______ __________ _________.
____ __________ ______ _____ ______ ____.
___ ______ __________ _______ ___ ___ _____.
___ __________ __________ ________ ___ ____ ______ ________ _____.
_________ ______ _____ ______.
Get Full Answer on WhatsApp
Let C be a binary code with a generator matrix each of whose rows has even weight. Show that, every codeword of C has even weight.
(Hint: Why is it enough to prove that sum of vectors of even weight in is a vector of even weight?)
Let C1 and C2 be two binary codes with generator matrices
respectively.
a) Find the minimum distance of both the codes.
b) Find the generator matrix of the code
C = {(u|u+v)|u ∈ C1,v ∈ C2}
obtained from C1 and C2 by (u|u+v) construction. Also, find the minimum distance of C .
Let a be a root of x² + 1 = 0 in .
a) Check whether α is a primitive element of . If it is not a primitive element in
find a primitive element γ in
in terms of a.
b) Make a table similiar to Table 5.1 on page 184 for with the primitive element y
c) Factorise x8 over .
d) Find all the possible generator polynomials of a [8, 6] cyclic code.
Find the minimum distance for each of the codes.
Let C1 and C2 be cyclic codes over , with generator polynomials g₁ (x) and g2(x), respectively. Prove that C1
C2 if and only if g2(x) | g1(x).
Find the convolutional code for the message 11011. The convolutional encoder is given in
Fig. 1.
The aim of this exercise is to show that every binary repetition code of odd length is perfect.
i) Find the value of t and d for a perfect code of length 2m + 1, m ∈ .
ii) Show that
(Hint: Start with the relation
iii) Deduce that every repetiition code of odd length is perfect.