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 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...
متن کاملEnumeration and construction of additive cyclic codes over Galois rings
Let R = GR(p, l) be a Galois ring of characteristic p and cardinality pεl, where p and l are prime integers. First, we give a canonical form decomposition for additive cyclic codes over R. This decomposition is used to construct additive cyclic codes and count the number of such codes, respectively. Thenwe give the trace dual code for each additive cyclic code over R from its canonical form dec...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2012
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2012.08.031