On a class of optimal constant weight ternary codes

Abstract

A weighing matrix W of order \(n=\frac{p^{m+1}-1}{p-1}\) and weight \(p^m\) is constructed and shown that the rows of W and \(-W\) together form optimal constant weight ternary codes of length n, weight \(p^m\) and minimum distance \(p^{m-1}(\frac{p+3}{2})\) for each odd prime power p and integer \(m\ge 1\) and thus $$\begin{aligned} A_3\left( \frac{p^{m+1}-1}{p-1},p^{m-1}\big (\frac{p+3}{2}\big ),p^{m}\right) =2\big (\frac{p^{m+1}-1}{p-1}\big ). \end{aligned}$$