Codes satisfying the chain condition

Abstract

The authors considered weight hierarchies of codes satisfying the chain condition, they called these chain-good. First, they gave a set of simple necessary conditions for a sequence to be chain-good. They proved that given one chain-good sequence, there is an infinite set of chain-good sequences that can be constructed from this one sequence. Finally, they used this result to completely describe the sets of chain-good sequences of dimensions up to 5.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>