Exercise $271$ Let $C$ be the $21,13,d$ binary cyclic code with defining set $T=\{3,6,7,9,12,14,15,18\}.$ Find a lower bound on the minimum weight of $C$ using the BCH Bound, the Hartmann$-$Tzeng Bound, and the van Lint$-$Wilson Bounding Technique. Also using the van Lint$-$Wilson Bounding Technique, show that an odd weight codeword has weight at least $7.$ Hint: For the latter, note that ${}^0$ is not a root of an odd weight codeword.