Information on Result #731496
Linear OA(9130, 13138, F9, 32) (dual of [13138, 13008, 33]-code), using trace code based on linear OA(8165, 6569, F81, 32) (dual of [6569, 6504, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(28) [i] based on
- linear OA(8163, 6561, F81, 32) (dual of [6561, 6498, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(8157, 6561, F81, 29) (dual of [6561, 6504, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(9131, 13139, F9, 32) (dual of [13139, 13008, 33]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(9130, 6569, F9, 2, 32) (dual of [(6569, 2), 13008, 33]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(9130, 4379, F9, 3, 32) (dual of [(4379, 3), 13007, 33]-NRT-code) | [i] | ||
| 4 | Linear OOA(9130, 821, F9, 32, 32) (dual of [(821, 32), 26142, 33]-NRT-code) | [i] | OA Folding and Stacking | |