Steinitz classes of unimodular lattices (Q1826966)

Let \(l\) be a prime such that \(l\equiv 7\pmod 8\) and set \(n=l+1.\) The lattice \(D_{n}^{+}\) is the set \((a_{\infty },a_{0},\dots,a_{l-1})\) in \( \mathbb{R} ^{n}\) such that \(2a_{i}\in \mathbb{Z} \) with the same parity and \(\sum_{i}a_{i}\in 2 \mathbb{Z} .\) Let \(O= \mathbb{Z} (\frac{1}{2}(1+\sqrt{-l}))\) be the ring of integers of the number field \( \mathbb{Q} (\sqrt{-l}).\) In [Eur. J. Comb. 22, 1033--1045 (2001; Zbl 0993.05036)] the author proved that \(D_{n}^{+}\) is an \(O\)-module under a certain action involving a Paley matrix. In the paper under review the author determines the isomorphism classes of \(D_{n}^{+}\) as an \(O\)-module.