The dual codes of two families of BCH codes
H. Xu, Xia Wu, Wei Lu, Xiwang Cao · Finite Fields and Their Applications · 2025
In this paper, we present an infinite family of MDS codes over F 2 s and two infinite families of almost MDS codes over F p s for any prime p , by investigating the parameters of the dual codes of two families of BCH codes. Notably, these almost MDS codes include two infinite families of near MDS codes over F 3 s , resolving a conjecture posed by Geng et al. in 2022. Furthermore, we demonstrate that both of these almost MDS codes and their dual codes hold infinite families of 3-designs over F p s for any prime p . Additionally, we study the subfield subcodes of these families of MDS and near MDS codes, and provide several binary, ternary, and quaternary codes with best known parameters.