Equidistant arithmetic codes and character sums (Q1323876)

Arithmetic codes are designed to correct errors in computer arithmetic in \(\mathbb{Z}\setminus m\mathbb{Z}\), where \(m= r^ n \pm1\) (\(r\) is the radix of the machine). The weight of a word \(x\) is the minimal number of non-zero coefficients in the representation \(x\equiv \sum_{i=0}^{n-1} c_ i r^ i\), \(| c_ i|<r\). The author derives necessary conditions for the existence of cyclic arithmetic codes in which all non-zero words have equal weight. As a result, he shows no new codes with the properties exist for radix \(r=2\) or \(r=3\).