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We find a family of quantum error correcting codes of parameters $[[\\sum_{i=w+1}^m \\binom{m}{i}, \\sum_{i=0}^{w} \\binom{m}{i}, \\sum_{i=w+1}^{r+1} \\binom{r+1}{i}]]$ for any integers $ m > 2r$, $r > w \\ge 0$, by puncturing quantum Reed-Muller codes. 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