Name
Abstract | ||
|---|---|---|
We study trace codes with defining set $L,$ a subgroup of the multiplicative group of an extension of degree $m$ of the alphabet ring $mathbb{F}_3+umathbb{F}_3+u^{2}mathbb{F}_{3},$ with $u^{3}=1.$ These codes are abelian, and their ternary images are quasi-cyclic of co-index three (a.k.a. cubic codes). Their Lee weight distributions are computed by using Gauss sums. These codes have three nonzero weights when $m$ is singly-even and $|L|=frac{3^{3m}-3^{2m}}{2}.$ When $m$ is odd, and $|L|=frac{3^{3m}-3^{2m}}{2}$, or $|L|={3^{3m}-3^{2m}}$ and $m$ is a positive integer, we obtain two new infinite families of two-weight codes which are optimal. Applications of the image codes to secret sharing schemes are also given. |
Year | Venue | Field |
|---|---|---|
2016 | arXiv: Information Theory | Integer,Discrete mathematics,Abelian group,Combinatorics,Secret sharing,Multiplicative group,Gauss sum,Ternary operation,Mathematics,Alphabet |
DocType | Volume | Citations |
Journal | abs/1612.00914 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Minjia Shi | 1 | 2 | 7.25 |
| Daitao Huang | 2 | 0 | 0.34 |
| Patrick Solé | 3 | 636 | 89.68 |