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...
متن کاملA New Bound for Cyclic Codes Beating the Roos Bound
We use the algebraic structure of cyclic codes and some properties of the discrete Fourier transform to give a reformulation of several classical bounds for the distance of cyclic codes, by extending techniques of linear algebra. We propose a bound, whose computational complexity is polynomial bounded, which is a generalization of the Hartmann-Tzeng bound and the Betti-Sala bound. In the majori...
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 کاملBinary Images of Z2Z4-Additive Cyclic Codes
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. We study the binary images of Z2Z4-additive cyclic codes. We determine all Z2Z4-additive cyclic codes with odd β whose Gray images are linear binar...
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: Designs, Codes and Cryptography
سال: 2016
ISSN: 0925-1022,1573-7586
DOI: 10.1007/s10623-016-0198-3