Generalized b-Symbol Weights of Linear Codes and b-Symbol MDS Codes

Generalized pair weights of linear codes are generalizations minimum symbol-pair weights, which were introduced by Liu and Pan (2022) recently. can be used to characterize the ability protecting information in read wire-tap channels type II. In this paper, we introduce notion generalized $b$ -symbol over finite fields, is a generalization Hamming weights. We obtain some basic properties bounds called Singleton-like for As examples, calculate weight matrices simplex codes. provide necessary sufficient condition code MDS using generator matrix parity check code. Finally, isomorphism preserving between two obtained. corollary, get classical MacWilliams extension theorem when notation="LaTeX">$b=1$ .