Name
Abstract | ||
|---|---|---|
Let
<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m>2$ </tex-math></inline-formula>
be an integer and
<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula>
be an odd prime. We explore the minimum distance of
<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula>
-ary cyclic codes of length
<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n = 2(p^{m}-1)/(p-1)$ </tex-math></inline-formula>
with two zeros. A sufficient condition for such cyclic codes with minimum distance at least three is obtained. A class of optimal
<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula>
-ary cyclic codes with minimum distance four are presented. Four explicit constructions for such optimal cyclic codes are provided. The weight distribution of the dual of the cyclic code in the first construction is given. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1109/LCOMM.2019.2921330 | IEEE Communications Letters |
Keywords | Field | DocType |
Linear codes,Zinc,Hamming weight,Indexes,Error correction codes,Decoding | Integer,Prime (order theory),Discrete mathematics,Computer science,Cyclic code,Computer network,Weight distribution,Hamming weight,Decoding methods | Journal |
Volume | Issue | ISSN |
23 | 8 | 1089-7798 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Dengchuan Liao | 1 | 0 | 0.34 |
| Xiaoshan Kai | 2 | 83 | 9.90 |
| Shixin Zhu | 3 | 216 | 37.61 |
| Ping Li | 4 | 78 | 14.22 |