The weight hierarchies of product codes and outer product codes

摘要

In this thesis we study the weight hierarchy for two code constructions, the product and outer product.;In the case of the first construction, we determine the weight hierarchy of the product of some classically important codes. In particular, the weight hierarchy of the product of an m-dimensional even-weight code and the [24,12,8] extended Golay code is determined in terms of the weight hierarchies of the component codes. The weight hierarchy of an m-dimensional even weight code and the [8,4,4] extended Hamming code is determined similarly.;In the case of the second construction, the weight hierarchy of an outer product of two self-complementary codes is expressed as a function of the weight hierarchies of the component codes. An alternative method to calculate the r-th generalized Hamming weight (and so the weight heirarchy) of the first-order Reed-Muller code is given. The outer product of a self-complementary code and a non-self-complementary code is also is also discussed.