Abia State Polytechnic Finit Algebraic Structures Exam

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Let C be the binary linear code generated by the following matrix:
1 0 1 1 1 0 1
1 1 1 0 0 0 0
0 1 1 0 1 1 0
(a) Determine all codewords and the minimum distance between words
in C. Can C locate and correct all single errors? (Prove or give a
counterexample.)
(b) Determine the parity-check matrix for the code (that is, a matrix H
such that for all codewords c E C, HCT = 7).
(c) If x = (1110111) was a received message, decode x to the most
likely codeword, and determine if it is unique.