University of Isfahan Transactions on Combinatorics 2251-8657 4 3 2015 09 01 Nonexistence of two circulant weighing matrices of weight 81$^{1}$ 43 52 6225 10.22108/toc.2015.6225 EN K. T. Arasu Wright State University Kyle Bayes Wright State University Ali Nabavi Institute for Research in Fundamental Sciences (IPM) Journal Article 2014 04 28 ‎‎In this paper‎, ‎we prove the nonexistence of two weighing matrices of‎ ‎weight 81‎, ‎namely $CW(88,81)$ and $CW(99,81)$‎. ‎We will apply two‎ ‎very different methods to do so; for the case of $CW(88,81)$‎, ‎we‎ ‎will use almost purely counting methods‎, ‎while for $CW(99,81)$‎, ‎we‎ ‎will use algebraic methods‎. https://toc.ui.ac.ir/article_6225_af3067b9d7efcee63f730ffc3790c91d.pdf