A weighted version of a result of Hamada on minihypers and on linear codes meeting the Griesmer bound

Minihypers were introduced by Hamada to investigate linear codes meeting the Griesmer bound. Hamada (Bull Osaka Women’s Univ 24:1–47, 1985; Discrete Math 116:229–268, 1993) characterized the non-weighted minihypers having parameters , with k−1 > λ₁ > λ₂ > ... > λ _h ≥ 0, as the union of a λ₁-dimensional space, λ₂-dimensional space, ..., λ _h -dimensional space, which all are pairwise disjoint. We present in this article a weighted version of this result. We prove that a weighted -minihyper , with k−1 > λ₁ > λ₂ > ... > λ _h ≥ 0, is a sum of a λ₁-dimensional space, λ₂-dimensional space, ..., and λ _h -dimensional space. This research was supported by the Project Combined algorithmic and theoretical study of combinatorial structures between the Fund for Scientific Research Flanders-Belgium (FWO-Flanders) and the Bulgarian Academy of Sciences. This research is also part of the FWO-Flanders project nr. G.0317.06 Linear codes and cryptography.