A Justesen construction of binary concatenated codes that asymptotically meet the Zyablov bound for low rate

摘要

An explicit construction of a sequence of binary codes that asymptotically meet the Zyablov bound for rates lower than 0.30 is given by using Justesen's construction of concatenation. The outer codes are constructed from generalized Hermitian curves. These outer codes can be described without any algebraic geometry terminology, while the proofs of some properties deeply rely on algebraic geometry.