Let G- be a generator matrix for a block code (not necessarily a "good" code) a) b) c) What is th...
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?
Consider the (5,2) linear binary code, C, with linear space of codewords spanned by the codewords (1, 0, 1,1, 1) and (0, 1, 1, 1, 0). 4. Find all codewords in C, find the systematic generator matrix, G, and a parity check matrix, H, for the code. a. Determine dmin for the code and the code's weight distribution. Determine all codewords in the dual code, Cd . Find a systematic generator matrix, Ga, for the dual code, and corresponding parity...
1. Channel Coding We would like to add linear block code (3,6) using the generator matrix: 1 001 01 G-0 1 0 0 1 1 (a) (5 points) Determine the parity check matrix H (b) (20 points) What is the minimum distance of this code? How many error can this code correct? (c) (5 points) What is the code word for the data sequence 011000101111? (d) (20 points) If you receive the codeword 010001000010101010, what is the transmitted sequence?
Two questions,please! 7. Assume C is a linear code. Prove that G is a generator matrix for C if and only if the columns of G form a basis of C 8. Let V. W U be vector spaces over F of finite dimension and φ: V → W, t : W → U linear maps. Prove that Im(φ)-ker( ) holds if and only if ψφ-0 and dimF1m(φ)-dimF kere). 7. Assume C is a linear code. Prove that G is...