Abstract This article introduces Generalized Hyperderivative Reed–Solomon codes (GHRS codes), which generalize NRT Reed–Solomon codes. Its main results are as follows: (1) every GHRS code is MDS, (2) the dual of a GHRS code is also an GHRS code, (3) determine subfamilies of GHRS codes whose members are low-density parity-check codes (LDPCs), and (4) determine a family of GHRS codes whose members are quasi-cyclic. We point out that there are GHRS codes having all of these properties.

Giotto provides an abstract programmer's model for the implementation of embedded control systems with hard real-time constraints. A typical control application consists of periodic software tasks together with a mode-switching logic for enabling and disabling tasks. Giotto specifies time-triggered sensor readings, task invocations, actuator updates, and mode switches independent of any implementation platform. Giotto can be annotated with platform constraints such as task-to-host mappings, and task and communication schedules. The annotations are directives for the Giotto compiler, but they do not alter the functionality and timing of a Giotto program. By separating the platform-independent from the platform-dependent concerns, Giotto enables a great deal of flexibility in choosing control platforms as well as a great deal of automation in the validation and synthesis of control software. The time-triggered nature of Giotto achieves timing predictability, which makes Giotto particularly suitable for safety-critical applications.

Automatic control systems typically incorporate legacy code and components that were originally designed to operate independently. Furthermore, they operate under stringent safety and timing constraints. Current design strategies deal with these requirements and characteristics with ad hoc approaches. In particular, when designing control laws, implementation constraints are often ignored or cursorily estimated. Indeed, costly redesigns are needed after a prototype of the control system is built because of missed timing constraints and subtle transient errors. In this paper, we use the concepts of platform-based design to develop a methodology for the design of automatic control systems that builds in modularity and correct-by-construction procedures. We illustrate our strategy by describing the (successful) application of the methodology to the design of a time-based control system for a helicopter-based uninhabited aerial vehicle.