Constructions of MDS-convolutional codes

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 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 47, NO. 5, JULY 2001 2045 Constructions of MDS-Convolutional Codes Roxana Smarandache, Student Member, IEEE, Heide Gluesing-Luerssen, and Joachim Rosenthal, Senior Member, IEEE Abstract—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 and each degree . The construction is based on a well-known connection between quasi-cyclic codes and convolutional codes.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 and each degree . The construction is based on a well-known connection between quasi-cyclic codes and convolutional codes.