problem1 - University of California San Diego ECE 259A:...

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University of California San Diego ECE 259A: Problem Set #1 0 . Send an e-mail to avardy@ucsd.edu , stating your name, your general research interests, your research advisor (if you have one), and what brings you to the course on algebraic coding theory. 1 . An erasure is an error whose location is known. Prove that a code over q with minimum dis- tance d can correct τ errors and σ erasures, provided d 2 1 . 2 . Find all the binary linear MDS codes. Prove your answer. 3 . Consider the binary linear code de±ned by the generator matrix G 1 0 1 1 1 0 0 1 1 1 1 1 0 1 0 1 1 0 1 1 1 (a) Find a generator matrix for this code in systematic form. (b) Find a parity check matrix for this code. (c) What is the minimum distance of this code? 4 . Let be an n , k , 2 t 1 binary linear code with parity check matrix H . Let be a code of length n 1 obtained by appending to all the codewords x x 1 , x 2 , . . . x n an overall par- ity-check bit equal to x 1 x 2 x n . (a) Find the parameters of
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problem1 - University of California San Diego ECE 259A:...

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