Maximum-distance separable (MDS) convolutional codes are characterized through the property that the free distance attains the generalized Singleton bound. The existence of MDS convolutional codes was established by two of the authors by using methods from algebraic geometry. This correspondence provides an elementary construction of MDS convolutional codes for each rate k/n and each degree δ. The construction is based on a well-known connection between quasi-cyclic codes and convolutional codes.
|Number of pages
|IEEE Transactions on Information Theory
|Published - Jul 2001
Bibliographical noteFunding Information:
Manuscript received September 15, 1999; revised November 30, 2000. This work was supported in part by NSF under Grants DMS-96-10389 and DMS-00-72383. The work of R. Smarandache was supported by a fellowship from the Center of Applied Mathematics at the University of Notre Dame. J. Rosenthal was carrying out this work while he was a Guest Professor at EPFL in Switzerland. The material in this correspondence was presented in part at the 2000 IEEE International Symposium on Information Theory, Sorrento, Italy, June 25–30, 2000.
- Convolutional codes
- Generalized Singleton bound
- Maximum-distance separable (MDS) convolutional codes
ASJC Scopus subject areas
- Information Systems
- Computer Science Applications
- Library and Information Sciences