Feedback equivalence of convolutional codes over finite rings

Abstract

The approach to convolutional codes from the linear systems point of view provides us with effective tools in order to construct convolutional codes with adequate properties that let us use them in many applications. In this work, we have generalized feedback equivalence between families of convolutional codes and linear systems over certain rings, and we show that every locally Brunovsky linear system may be considered as a representation of a code under feedback convolutional equivalence.

Keywords

• convolutional codes
• linear systems
• feedback equivalence
• finite rings
• coding theory
• 94b10
• 93c05
• 13c10
• 93b20