Name
Abstract | ||
|---|---|---|
In this paper, we consider the problem of determining the weight spectrum of $q$ -ary codes $C(3,m)$ associated with Grassmann varieties $G(3,m)$. For $m=6$, this was done in a paper by Nogin in 1997. We derive a formula for the weight of a codeword of $C(3,m)$, in terms of certain varieties associated with alternating trilinear forms on $\\BBF_{q}^{m}$. The classification of such forms under the action of the general linear group $GL(m, \\BBF_{q})$ is the other component that is required to calculate the spectrum of $C(3,m)$. For $m=7$, we explicitly determine the varieties mentioned above. The classification problem for alternating three-forms on $\\BBF_{q}^{7}$ was solved in a study by Cohen and Helminck in 1988, which we then use to determine the spectrum of $C(3,7)$. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1109/TIT.2012.2219497 | IEEE Transactions on Information Theory |
Keywords | Field | DocType |
Grassmannian, Pfaffian, trilinear alternating forms, weight spectrum | Discrete mathematics,Combinatorics,General linear group,Code word,Grassmannian,Mathematics | Journal |
Volume | Issue | ISSN |
59 | 2 | 0018-9448 |
Citations | PageRank | References |
6 | 0.57 | 3 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Krishna V. Kaipa | 1 | 15 | 3.32 |
| Harish K. Pillai | 2 | 90 | 20.79 |