Enumeration of ${\rm AGL}(\frac m3, {\Bbb F}_{p^3})$-Invariant Extended Cyclic Codes
| dc.creator | Hou, Xiang-dong | |
| dc.date | 2009-05-26 | |
| dc.date.accessioned | 2026-07-07T13:18:27Z | |
| dc.date.available | 2026-07-07T13:18:27Z | |
| dc.description | Let $p$ be a prime and let $r, e, m$ be positive integers such that $r|e$ and $e|m$. The enumeration of linear codes of length $p^m$ over ${\Bbb F}_{p^r}$ which are invariant under the affine linear group ${\rm AGL}(\frac me, {\Bbb F}_{p^e})$ is equivalent to the enumeration of certain ideals in a partially ordered set $({\mathcal U}, \prec)$ where ${\mathcal U}=\{0,1,...,\frac me(p-1)\}^e$ and $\prec$ is defined by an $e$-dimensional simplicial cone. When $e=2$, the enumeration problem was solved in an earlier paper. In the present paper, we consider the cases $e=3$. We describe methods for enumerating all ${\rm AGL}(\frac m3, {\Bbb F}_{p^3})$-invariant linear codes of length $p^m$ over ${\Bbb F}_{p^r}$ | |
| dc.description | 42 pages, 30 figures | |
| dc.identifier | https://arxiv.org/abs/0905.4288 | |
| dc.identifier | http://arxiv.org/abs/0905.4288 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/231436 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A99; 94B27 | |
| dc.title | Enumeration of ${\rm AGL}(\frac m3, {\Bbb F}_{p^3})$-Invariant Extended Cyclic Codes | |
| dc.type | text |