Bounds for the $l_1$-distance of $q$-ary lattices obtained via Constructions D, D$^{'}$ and $\overline{D}$
نویسندگان
چکیده
Lattices have been used in several problems in coding theory and cryptography. In this paper we approach q-ary lattices obtained via Constructions D, D′ and D. It is shown connections between Constructions D and D′. Bounds for the minimum l1-distance of lattices ΛD, ΛD′ and ΛD and, under certain conditions, a generator matrix for ΛD′ are presented. In addition, when the chain of codes used is closed under the zero-one addition, we derive explicit expressions for the minimum l1-distances of the lattices ΛD and ΛD attached to the distances of the codes used in these constructions.
منابع مشابه
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عنوان ژورنال:
- CoRR
دوره abs/1611.00435 شماره
صفحات -
تاریخ انتشار 2016