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# hw0 - Error Correcting Codes Combinatorics Algorithms and...

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Error Correcting Codes: Combinatorics, Algorithms and Applications Spring 2011 Homework 0 The problems in this homework are to help you get more comfortable with the background material. Most of these questions would be useful in solving the real homework problems. Please do not submit answers to these questions. I have made the problem statements verbose so that they are somewhat self-sufficient. Unlike the real homework problems, for these problem, feel free to refer to any source that might help you. This document might be updated with more problems as the semester moves on. 1. ( System of Linear Equations ) In this problem we will look at the problem of solving a system of linear equations over F q . That is, one needs to solve for unknowns x 1 , . . . , x n given the following m linear equations (where a i,j , b i F q for 1 i m and 1 j n ): a 1 , 1 x 1 + a 1 , 2 x 2 + · · · + a 1 ,n x n = b 1 . a 2 , 1 x 1 + a 2 , 2 x 2 + · · · + a 2 ,n x n = b 2 .

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