For enhancement of the quality of digital transmissions, standards are in continual evolution, which generates compatibility problems. Cognitive radio systems permit one to solve this problem through the design of intelligent receivers. However, such receivers must be able to adapt themselves to a specific transmission context. This requires the development of new methods in order to blindly estimate error-correcting codes. Coding schemes such as turbocode, composed of convolutional codes, belong to a family of error-correcting codes in use in many standards. In most of the methods designed to identify convolutional encoders the algebraic properties are used implicitly. However usually, these dedicated properties are neither explicated, nor detailed, nor demonstrated. The study reported here investigates the algebraic properties of convolutional encoders, useful for blind recognition methods in the cognitive radio context and more specially the algebraic relationships between different forms of a convolutional code and its corresponding dual code. Moreover, some simulation results are presented to show the relevance of these properties for the blind identification of the convolutional encoder.