1
$\begingroup$

$\mathcal L$ and $\mathcal L'$ be full rank lattices in $\mathbb R^n$ with shortest vectors $v_1,\dots,v_n$ and $v_1',\dots,v_n'$ respectively where $$\|v_1\|_2\leq\dots\leq\|v_n\|_2$$ $$\|v_1'\|_2\leq\dots\leq\|v_n'\|_2$$ hold and $\mathcal L'=Span(v_1,\dots,v_n)$ and $\mathcal L=Span(v_1',\dots,v_n')$.

  1. Do the shortest vectors of $\mathcal L\otimes\mathcal L'$ have any relation to shortest vectors of $\mathcal L$ and $\mathcal L'$ and what is the span of $v_i\otimes v_j'$?

  2. Do maximal lattices in $\mathcal L\otimes\mathcal L'$ have any relation to $\mathcal L$ and $\mathcal L'$ and $v_1,\dots,v_n$ and $v_1',\dots,v_n'$?

$\endgroup$

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.