Name
Abstract | ||
|---|---|---|
Let $\mathbb{F}_{2^m}$ be a finite field of characteristic $2$ and $R=\mathbb{F}_{2^m}[u]/\langle u^k\rangle=\mathbb{F}_{2^m} +u\mathbb{F}_{2^m}+\ldots+u^{k-1}\mathbb{F}_{2^m}$ ($u^k=0$) where $k\in \mathbb{Z}^{+}$ satisfies $k\geq 2$. For any odd positive integer $n$, it is known that cyclic codes over $R$ of length $2n$ are identified with ideals of the ring $R[x]/\langle x^{2n}-1\rangle$. In this paper, an explicit representation for each cyclic code over $R$ of length $2n$ is provided and a formula to count the number of codewords in each code is given. Then a formula to calculate the number of cyclic codes over $R$ of length $2n$ is obtained. Moreover, the dual code of each cyclic code and self-dual cyclic codes over $R$ of length $2n$ are investigated. (AAECC-1522) |
Year | Venue | DocType |
|---|---|---|
2015 | CoRR | Journal |
Volume | Citations | PageRank |
abs/1511.05413 | 0 | 0.34 |
References | Authors | |
3 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yonglin Cao | 1 | 46 | 15.88 |
| Yuan Cao | 2 | 548 | 35.60 |
| Fu Fang-Wei | 3 | 381 | 57.23 |