Name
Abstract | ||
|---|---|---|
Professor Cunsheng Ding gave cyclotomic constructions of cyclic codes with length being the product of two primes. In this paper, we study the cyclic codes of length $n=2^e$ and dimension $k=2^{e-1}$. Clearly, Dingu0027s construction is not hold in this place. We describe two new types of generalized cyclotomy of order two, which are different from Dingu0027s. Furthermore, we study two classes of cyclic codes of length $n$ and dimension $k$. We get the enumeration of these cyclic codes. Whatu0027s more, all of the codes from our construction are among the best cyclic codes. Furthermore, we study the hull of cyclic codes of length $n$ over $mathbb{F}_q$. We obtain the range of $ell=dim({rm Hull}(C))$. We construct and enumerate cyclic codes of length $n$ having hull of given dimension. |
Year | Venue | Field |
|---|---|---|
2018 | arXiv: Information Theory | Discrete mathematics,Finite field,Enumeration,Hull,Mathematics |
DocType | Volume | Citations |
Journal | abs/1808.06338 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Binbin Pang | 1 | 6 | 0.85 |
| Shixin Zhu | 2 | 216 | 37.61 |
| Ping Li | 3 | 322 | 42.76 |