English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We describe odd-length-cube tilings of the n-dimensional q-ary torus whatincludes q-periodic integer lattice tilings of R^n. In the language of codingtheory these tilings correspond to perfect codes with respect to the maximummetric. A complete characterization of the two-dimensional tillings ispresented and in the linear case, a description of general matrices, isometryand isomorphism classes is provided. Several methods to construct perfect codesfrom codes of smaller dimension or via sections are derived. We introduce aspecial type of matrices (perfect matrices) which are in correspondence withgenerator matrices for linear perfect codes in arbitrary dimensions. Formaximal perfect codes, a parametrization obtained allows to describeisomorphism classes of such codes. We also approach the problem of whatisomorphism classes of abelian groups can be represented by q-ary n-dimensionalperfect codes of a given cardinality N.

On Cube Tilings of Tori and Classification of Perfect Codes in the Maximum Metric