We present Tracs, a dual-sided see-through display system with controllable transparency. Traditional displays are a constant visual and communication barrier, hindering fast and efficient collaboration of spatially close or facing co-workers. Transparent displays could potentially remove these barriers, but introduce new issues of personal privacy, screen content privacy and visual interference. We therefore propose a solution with controllable transparency to overcome these problems. Tracs consists of two see-through displays, with a transparency-control layer, a backlight layer and a polarization adjustment layer in-between. The transparency-control layer is built as a grid of individually addressable transparency-controlled patches, allowing users to control the transparency overall or just locally. Additionally, the locally switchable backlight layer improves the contrast of LCD screen content. Tracs allows users to switch between personal and collaborative work fast and easily and gives them full control of transparent regions on their display.

In this correspondence, we investigate the covering radius of codes over Z/sub 4/ for the Lee and Euclidean distances in relation with those of binary nonlinear codes and lattices obtained by the Gray map and Construction A/sub 4/, respectively. We give several upper and lower bounds on covering radii, including Z/sub 4/-analogs of the sphere-covering bound, the packing radius bound, the Delsarte bound, and the redundancy bound. We show that any Euclidean-optimal Type II code of length 24 has covering radius 8 with respect to the Euclidean distance. We determine the covering radius of the Klemm codes with respect to the Lee distance. We derive lower bounds on the covering radii of the Niemeier lattices.