$ \mathbb{Z}_{4}\mathbb{Z}_{4}[u] $-additive cyclic and constacyclic codes
نویسندگان
چکیده
منابع مشابه
Cyclic additive codes and cyclic quantum stabilizer codes
The theory of cyclic linear codes in its ring-theoretic formulation is a core topic of classical coding theory. A simplified approach is in my textbook [1]. The language of ring theory is not needed. We will present a self-contained description of the more general theory of cyclic additive codes using the same method. This includes cyclic quantum stabilizer codes as a special case. The basic in...
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In this study, we consider linear and especially cyclic codes over the non-chain ring Zp[v]/〈v − v〉 where p is a prime. This is a generalization of the case p = 3. Further, in this work the structure of constacyclic codes are studied as well. This study takes advantage mainly from a Gray map which preserves the distance between codes over this ring and p-ary codes and moreover this map enlighte...
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Constacyclic codes may naturally be viewed as objects arising from the cohomological concept of a cocycle. Cohomology theory suggests a transformation which is used to show, under certain circumstances, a cyclic code of length mn over a ring R is isomorphic to the direct sum of m constacyclic codes of length n. In particular this isomorphism holds in many local rings (for example Galois rings) ...
متن کاملℤ2ℤ4-Additive Cyclic Codes: Kernel and Rank
A Z2Z4-additive code C ⊆ Z α 2 ×Z 4 is called cyclic if the set of coordinates can be partitioned into two subsets, the set of Z2 and the set of Z4 coordinates, such that any cyclic shift of the coordinates of both subsets leaves the code invariant. Let Φ(C) be the binary Gray image of C. We study the rank and the dimension of the kernel of a Z2Z4-additive cyclic code C, that is, the dimensions...
متن کاملZ2Z4-additive cyclic codes, generator polynomials and dual codes
A Z2Z4-additive code C ⊆ Z2 ×Zβ4 is called cyclic if the set of coordinates can be partitioned into two subsets, the set of Z2 and the set of Z4 coordinates, such that any cyclic shift of the coordinates of both subsets leaves the code invariant. These codes can be identified as submodules of the Z4[x]-module Z2[x]/(x− 1)×Z4[x]/(x − 1). The parameters of a Z2Z4-additive cyclic code are stated i...
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ژورنال
عنوان ژورنال: Advances in Mathematics of Communications
سال: 2020
ISSN: 1930-5338
DOI: 10.3934/amc.2020094