Finite Frame as Code: Some Characterizations for Error Correction Codes and Three Algorithms for Troubleshooting in Data Transfer

"Linear codes in coding theory need matrices whose rows form a basis for a finite dimensional space. In this paper, after introducing some preliminaries about frames, we state the idea of using finite frames    instead of basis for encoding of information and then we introduce some frames which their related linear codes are useful in finding and correcting errors in data transfer. A number of methods for producing    examples of such frames are presented using some well-known frame types and we show specifically that the families of frames which have been considered in some papers can be extended. Finally, we modify the idea of encoding to facilitate the use of approximate and generalized duals for decoding of received information. Also, some algorithms for decoding of frame coefficients with erasures are proposed.