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- W3153225494 abstract "For a given subset $Asubseteq mathbb F_q^*$, we study the problem of finding a large packing set $B$ of $A$, that is, a set $B subseteq mathbb F_q^*$ such that $|AB|=|A||B|$. We prove the existence of such a $B$ of size $|B|ge (q-1)/|A/A|$ and show that this bound is in general optimal. The case that $q=p$ is a prime and $A={1,2,ldots,lambda}$ for some positive integer $lambda$ is particularly interesting in view of the construction of limited-magnitude error correcting codes. Here we construct a packing set $B$ of size $|B|gg p (lambda log p)^{-1}$ for any $lambda le c p^{1/2}$ for some explicitly calcuable constant $c$. This result is optimal up to the logarithmic factor." @default.
- W3153225494 created "2021-04-26" @default.
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- W3153225494 date "2016-11-02" @default.
- W3153225494 modified "2023-09-27" @default.
- W3153225494 title "Packing Sets" @default.
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- W3153225494 hasPublicationYear "2016" @default.
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