Effective module lattices and their shortest vectors
CoRR(2024)
摘要
We prove tight probabilistic bounds for the shortest vectors in module
lattices over number fields using the results of arXiv:2308.15275. Moreover,
establishing asymptotic formulae for counts of fixed rank matrices with
algebraic integer entries and bounded Euclidean length, we prove an approximate
Rogers integral formula for discrete sets of module lattices obtained from
lifts of algebraic codes. This in turn implies that the moment estimates of
arXiv:2308.15275 as well as the aforementioned bounds on the shortest vector
also carry through for large enough discrete sets of module lattices.
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