DIMENSION LENGTH PROFILES AND TRELLIS COMPLEXITY OF LINEAR BLOCK-CODES

This semi-tutorial paper discusses the connections between the dimensi on/length profile (DLP) of a linear code, which is essentially the sam e as its ''generalized Hamming weight hierarchy'' [1], and the complex ity of its minimal trellis diagram. These connections are close and de ep. DLP duality is closely related to trellis duality. The DLP of a co de gives tight bounds on its state and branch complexity profiles unde r any coordinate ordering; these bounds can often be met. A maximum di stance separable (MDS) code is characterized by a certain extremal DLP , from which the main properties of MDS codes are easily derived. The simplicity and generality of these interrelationships are emphasized.