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Double circulant codes from two class association schemes
On blocking sets in projective Hjelmslev planes
1. | Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev str. bl. 8, Sofia 1113, Bulgaria |
In case of chain rings $R$ with $|R| = q^2, R$∕rad$R \cong \mathbb F_q$ and $n = 1$, we prove that the size of the second smallest irreducible $(k, 1)$-blocking set is $q^2 + q + 1$. We classify all blocking sets with this cardinality. It turns out that if char$R = p$ there exist (up to isomorphism) two such sets; if char$R = p^2$ the irreducible $(q^2 + q + 1, 1)$-blocking set is unique. We introduce a class of irreducible $(q^2 + q + s, 1)$ blocking sets for every $s \in {1, \cdots , q + 1}$. Finally, we discuss briefly the codes over $\mathbb F_q$ obtained from certain blocking sets.
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