Name
Abstract | ||
|---|---|---|
We construct a class of $\mathbb {Z}_{p}\mathbb {Z}_{p^{s}}$-additive cyclic codes generated by pairs of polynomials, where p is a prime number. The generator matrix of this class of codes is obtained. By establishing the relationship between the random $\mathbb {Z}_{p}\mathbb {Z}_{p^{s}}$-additive cyclic code and random quasi-cyclic code of index 2 over $\mathbb {Z}_{p}$, the asymptotic properties of the rates and relative distances of this class of codes are studied. As a consequence, we prove that $\mathbb {Z}_{p}\mathbb {Z}_{p^{s}}$-additive cyclic codes are asymptotically good since the asymptotic GV-bound at $\frac {1+p^{s-1}}{2}\delta $ is greater than $\frac {1}{2}$, the relative distance of the code is convergent to δ, while the rate is convergent to $\frac {1}{1+p^{s-1}}$ for $0< \delta < \frac {1}{1+p^{s-1}}$. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1007/s12095-019-00397-z | Cryptography and Communications |
Keywords | Field | DocType |
-additive cyclic codes, Generator matrix, Random codes, GV-bound, Asymptotically good codes, 94B05, 94B15 | Discrete mathematics,Combinatorics,Generator matrix,Prime number,Cyclic code,Mathematics | Journal |
Volume | Issue | ISSN |
12 | 2 | 1936-2447 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ting Yao | 1 | 1 | 0.70 |
| Shixin Zhu | 2 | 216 | 37.61 |