Information on Result #731366
Linear OA(958, 13138, F9, 14) (dual of [13138, 13080, 15]-code), using trace code based on linear OA(8129, 6569, F81, 14) (dual of [6569, 6540, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- linear OA(8127, 6561, F81, 14) (dual of [6561, 6534, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(8121, 6561, F81, 11) (dual of [6561, 6540, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(812, 8, F81, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,81)), using
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
- Reed–Solomon code RS(79,81) [i]
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(959, 13139, F9, 14) (dual of [13139, 13080, 15]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(958, 13138, F9, 2, 14) (dual of [(13138, 2), 26218, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(958, 13138, F9, 3, 14) (dual of [(13138, 3), 39356, 15]-NRT-code) | [i] | ||
| 4 | Digital (44, 58, 13138)-net over F9 | [i] | ||
| 5 | Linear OOA(958, 6569, F9, 2, 14) (dual of [(6569, 2), 13080, 15]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(958, 4379, F9, 3, 14) (dual of [(4379, 3), 13079, 15]-NRT-code) | [i] | ||