ref the question: https://www.homeworklib.com/question/1427779/1-consider-a-155-linear-block-code-cyclic-in
Consider a (15,5) linear block code (cyclic) in systematic form. The generator polynomial is given as g(x)=1+X+X^2+X^5+X^8+X^10.
1) Consider a (15,5) linear block code (cyclic) in systematic form. The generator polynomial is given as g(x) = 1 + x + x2 + x5 + x + x10. a. Design and draw the circuit of the feedback shift register encoder and decoder (6 Marks) b. Use the encoder obtained in part a to find the code word for the message (10110). (Assume the right most bit is the earliest bit) (5 Marks) C. Repeat the steps of part...
1) Consider a (15,5) linear block code (cyclic) in systematic form. The generator polynomial is given as. g(x) = 1 + x + x2 + x5 + x + x10. a. Design and draw the circuit of the feedback shift register encoder and decoder.(6 Marks) b- Use the encoder obtained in part a to find the code word for the message (11101] (Assume the right most bit is the earliest bit) (5 Marks) c- Repeat the steps of part b...
(c) Consider the (7, 4) Hamming Code defined by the generator polynomial g(x)-1 +x+x'. The code word 1000101 is sent over a noisy channel, producing the received word 0000101 that has a single error. Determine the syndrome polynomial s(x) for this received word. Find its corresponding message vector m and express m in polynomial m(x). 0
1. (30 points) Consider the systematic binary linear (6,3) code with generator matrix 1 0 01 1 0 G- 0 1 0 0 1 1 a) Determine the parity check matrix H of the code. b) What is the minimum distance of the code? How many errors can this code correct and detect? c) Show the results in b) using decoding table d) Find the most likely codeword, given that the noisy received codeword is 010101. e) Now suppose 001101...
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Consider a CRC code with a generator polynomial of g(x) -xSx21 a. (15 points) Show step by step (using the longhand division) how to find the codeword that corresponds to information bits of 10011 b. (15 points) Show the shift-register circuit that implements this CRC code. C. Suppose the codeword length is 10. Answer the following questions, with proper justifications i. (10 points) Give an example of undetectable error burst of length 9 ii....
Consder the (7,4) cyclic code having the generator ploynomial G(x) = x3 +x2 + 1. a) What is the binary representation of G (x)? [15 Marks) b) Assume that the messgae is M(x) = (1 00 1). Determine the Block Check Code (BCC) mathemetically c) What is the transmitted codeword? d) Assume the received codeword is (1101110). Determine the corresponding syndrome. 11o NIO loooo1 bits There are e( r0s are deteted ron ceceeted Code we the e) Does the received...
Consider T:R4 → R3 with 1 [T) 3 2 -4-1 0 0 5 7 8 10 4 3 -20 -6 1 0 0 5 om Find a basis for image(T). What is dim(image(T))? Convert image(T) to relation form.
Consider the 2-error correcting RS code over GF(8). Let α be a primitive element of GF(8). (a) List the parameters of the code. Find the generator polynomial of the code. Encode the message [1 α α2 ] systematically. (b) List the parameters of the binary expanded code. Provide binary equivalents of the encoding above. (c) Decode the received word [0 1 α α2 α3 1 0].
Write the cubic polynomial function f(x)in expanded form with zeros −5, −2,and 2, given that f(−1)= −24. f (x) = ______ Suppose $3,500 is compounded annually for 42 years. If no other deposits are made, what rate is needed for the balance to triple in that time? Round the answer to the nearest hundredth of a percent. Interest Rate = _______%