## On classifying Minkowskian sublattices. With an Appendix by Mathieu Dutour Sikirić.(English)Zbl 1329.11071

Summary: Let $$\Lambda$$ be a lattice in an $$n$$-dimensional Euclidean space $$E$$ and let $$\Lambda^{\prime}$$ be a Minkowskian sublattice of $$\Lambda$$, that is, a sublattice having a basis made of representatives for the Minkowski successive minima of $$\Lambda$$. We extend the classification of possible $$\mathbb Z/d\mathbb Z$$-codes of the quotients $$\Lambda/\Lambda^{\prime}$$ to dimension 9, where $$d\mathbb Z$$ is the annihilator of $$\Lambda/\Lambda^{\prime}$$.

### MSC:

 11H55 Quadratic forms (reduction theory, extreme forms, etc.) 11H71 Relations with coding theory 94B05 Linear codes (general theory)

### Keywords:

Euclidean lattices; quadratic forms; linear codes

### Software:

Convex; Polyhedral
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