Canonization of linear codes over $\mathbb Z$<SUB><I>4</I></SUB>
نویسندگان
چکیده
منابع مشابه
Some Results on Linear Codes over $\mathbb{Z}_4+v\mathbb{Z}_4$
In this paper, we study the linear codes over the commutative ring R = Z4 + vZ4, where v2 = v. We define the Gray weight of the elements of R and give a Gray map from Rn to Z2n 4 , which lead to the MacWillams identity of the linear code over R. Some useful results on self-dual code over R are given. Furthermore, the relationship between some complex unimodular lattices and Hermitian self-dual ...
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In this paper, we construct an infinite family of five-weight codes from trace codes over the ring R = F2+uF2, where u 2 = 0. The trace codes have the algebraic structure of abelian codes. Their Lee weight is computed by using character sums. Combined with Pless power moments and Newton’s Identities, the weight distribution of the Gray image of trace codes was present. Their support structure i...
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In this paper, we have studied cyclic codes over the ring R = Z4 +uZ4, u = 0. We have considered cyclic codes of odd lengths. A sufficient condition for a cyclic code over R to be a Z4-free module is presented. We have provided the general form of the generators of a cyclic code over R and determined a formula for the ranks of such codes. In this paper we have mainly focused on principally gene...
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Let r, s, t be three positive integers and C be a binary linear code of lenght r + s + t. We say that C is a triple cyclic code of lenght (r, s, t) over Z 2 if the set of coordinates can be partitioned into three parts that any cyclic shift of the coordinates of the parts leaves invariant the code. These codes can be considered as Z 2 [x]-submodules of Z2[x] x r −1 × Z2[x] x s −1 × Z2[x] x t −1...
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ژورنال
عنوان ژورنال: Advances in Mathematics of Communications
سال: 2011
ISSN: 1930-5346
DOI: 10.3934/amc.2011.5.245