On the Generalized Hamming Weights of Convolutional Codes

Motivated by applications in cryptology, Wei introduced in 1991 the concept of a generalized Hamming weight for a linear block code. In this correspondence, we define generalized Hamming weights for the class of convolutional codes and we derive several of their basic properties. By restricting to convolutional codes having a generator matrix G(D) with bounded Kronecker indices we are able to derive upper and lower bounds on the weight hierarchy. Index Terms--- Convolutional codes, generalized Hamming weights, weight hierarchy, length/dimension profile. I. INTRODUCTION An important set of code parameters defined for a linear block code are the so-called generalized Hamming weights first introduced by Wei in [1]. By definition, the rth generalized Hamming weight dr (C) of a linear block code C is equal to the smallest support of any r-dimensional subcode of C. In particular, d0 (C)=0and d1 (C) is equal to the distance of C. In this way, every [n; k] linear block code has associated..