Density/length profiles and trellis complexity of linear block codes and lattices

Abstract

The dimension/length profile (DLP) of a linear code C is equivalent to its generalized Hamming weight (GHW) hierarchy. The trellis complexity of C is intimately related to its DLP; indeed, these two topics should be regarded as parts of the same subject. Using this concept,easy proofs of unknown results and some new results are given. An analogous concept is introduced for lattices, the density/length profile (DLP). Analogous results are derived, which however look quite different.<>