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| 摘要: |
| 本文研究了环$R=\FF_2+u\FF_2+v\FF_2+uv\FF_2$上长为2^s所有常环码。借助$R$是局部环,完全刻画每类常环码的生成元。 |
| 关键词: 常循环码 循环码 局部环 重根常循环码 |
| DOI： |
| 分类号:94B05; 94B15; 11T71 |
| 基金项目: |
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| Constacyclic Codes of length $2^s$ over $\mathbb F_{2}+u\mathbb F_{2}+v\mathbb F_{2}+uv\mathbb F_{2}$ |
|
刘修生
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| Abstract: |
| The ring $R=\FF_2+u\FF_2+v\FF_2+uv\FF_2$ is a local ring, but it is
not a chain ring, because it contains precisely 8 units, namely,
$a_0+a_1u+a_2v+a_3uv$, where $a_0,a_1,a_2, a_3\in \FF_2,a_0=1,
a_1,a_2,a_3 \in \{0,1\}.$ In this paper, we investigate all
constacyclic codes of length $2^s$ over $R$. Firstly, we classify
all cyclic and $(1+uv)-$constacyclic codes of length $2^s$ over $R$,
and obtain their structure in each of those cyclic and
$(1+uv)-$constacyclic codes. Secondly, we address the
$(1+u)-$constacyclic codes of length $2^s$ over $R$, and get their
classification and structure. Finally, using similar discussion of
$(1+u)-$constacyclic codes, we obtain the classification and the
structure of
$(1+v),(1+u+uv),(1+v+uv),(1+u+v),(1+u+v+uv)-$constacyclic codes of
length $2^s$ over $R$. |
| Key words: constacyclic codes cyclic codes local ring Repeated-root constacyclic codes |
