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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)

Software:

Convex; Polyhedral
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References:

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