HKZ reduced

Definition

Let $\pi_i$ as the projection to the orthogonal complement of $\left\{b_j\right\}_{j=1}^{i-1}$ .Then the basis is HKZ-reduced if it is size-reduced and $||b_i^*||=\lambda_1\left(\pi_i(L)\right)$ . This definition gives us a relatively simple way to compute a HKZ-reduced basis by iteratively finding the shortest vector in orthogonal projections.

Bounds

\frac4{i+3}\leq\left(\frac{||b_i||}{\lambda_i(L)}\right)^2\leq\frac{i+3}4

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Last updated 3 years ago

Definition

Let

\pi_i

as the projection to the orthogonal complement of

\left\{b_j\right\}_{j=1}^{i-1}

.Then the basis is HKZ-reduced if it is size-reduced and

||b_i^*||=\lambda_1\left(\pi_i(L)\right)

. This definition gives us a relatively simple way to compute a HKZ-reduced basis by iteratively finding the shortest vector in orthogonal projections.