Wireless Sensor Networks (WSN) consist of low powered and resource constrained sensor nodes which are left unattended for long duration of time. Hence it is very challenging to design and implement cost effective security protocols for such networks. Thus symmetric key cryptographic techniques are preferred over public key techniques for communication in such scenarios. Prior to deployment, keys are usually predistributed into the nodes and this problem has been well studied. Highlighting that connectivity and communication are two separate aspects of a WSN, we propose a secure connectivity model using Reed Muller codes. The model is then utilized to securely establish communication keys and exchange messages in a WSN designed on the basis of a scheme that uses affine planes for key predistribution. Novel combination of both the ideas yields highly resilient communication model with full connectivity between nodes.