Consider the 2-error correcting, narrow-sense RS code over GF(16) (α is a primitive element). (a) Write down the generator polynomial and the parity check polynomial. (b) Provide a parity check matrix for the code. (c) Decode the received vector V = [α6 α12 α9 α12 0 0 0 α8 0 0 0 α10 α α13 α].
Consider the 2-error correcting, narrow-sense RS code over GF(16) (α is a primitive element). (a) Write down the generator polynomial and the parity check polynomial. (b) Provide a parity check matrix...
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].
Consider a (7, 4) code whose generator matrix isa) Find all the codewords of the code b) Find H, the parity check matrix of the code. c) Compute the syndrome for the received vector 1 101 1 0 1. Is this a valid code vector? d) What is the error-correcting capability of the code? e) What is the error-detecting capability of the code?
Find the generator polynomial of the length-1023, primitive binary BCH code with designed error-correcting capability (a) t = 1. (b) t = 2. (c) t = 3. (d) t = 4.
coding theory 1. If 100 031 Go 01 0 0 9 0001 27 01 0 054 is a generator matrix for a linear code over Fi encode the message stream m(2, 3,9, 6, 1,4,3, 8) (by breaking it into encodable pieces). 2. If T (1 0 1 2 3 4 be the transpose of a parity-check matrix for a perfect 1-error-correcting code over Fs, with implicit generator matrix 4410 0 0 3 4 0 1 0 0 1400 01 1....