Abstract
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 \(\{\sum_{i=1}^h v_{\lambda_i+1},\sum_{i=1}^h v_{\lambda_i};k-1,q\}\), 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 \(\{\sum_{i=1}^h v_{\lambda_i+1},\sum_{i=1}^h v_{\lambda_i};k-1,q\}\)-minihyper \({\mathfrak{F}}\) , with k−1 > λ1 > λ2 > ... > λ h ≥ 0, is a sum of a λ1-dimensional space, λ2-dimensional space, ..., and λ h -dimensional space.
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Communicated by: S. Ball.
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.
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Landjev, I., Storme, L. A weighted version of a result of Hamada on minihypers and on linear codes meeting the Griesmer bound. Des. Codes Cryptogr. 45, 123–138 (2007). https://doi.org/10.1007/s10623-007-9093-2
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DOI: https://doi.org/10.1007/s10623-007-9093-2