q-ary lattices in the lp norm and a generalization of the Lee metric
نویسندگان
چکیده
q-ary lattices are obtained from linear q-ary codes via the so-called Construction A. We study these lattices in the lp norm in R and the associated q-ary codes in the induced p-Lee metric in Zq . This induced metric extends to 1 ≤ p < ∞ the well-known Lee metric when p = 1. A previous result on lattice decoding in the Lee metric is generalized for p > 1 and the existence of perfect codes in such metrics is briefly discussed. In the case p =∞ a complete characterization of perfect codes is given.
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