Abstract
We use some basic results and ideas from the integral geometry to study certain properties of group codes. The properties being studied are generalized weights and spectra of linear block codes over a finite field and their analogues for lattice sphere packings in Euclidean space. No new results are obtained about linear codes, although several short and simple proofs for known results are given. As to the lattices, we introduce a generalization of lattice Θ-functions, prove several identities on these functions, and prove generalizations of Siegel mean value and Minkowski–Hlawka theorems.
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