Information on Result #699581
Linear OA(8175, 6587, F81, 34) (dual of [6587, 6512, 35]-code), using construction X applied to Ce(33) ⊂ Ce(24) based on
- linear OA(8167, 6561, F81, 34) (dual of [6561, 6494, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(8149, 6561, F81, 25) (dual of [6561, 6512, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(818, 26, F81, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,81)), using
- discarding factors / shortening the dual code based on linear OA(818, 81, F81, 8) (dual of [81, 73, 9]-code or 81-arc in PG(7,81)), using
- Reed–Solomon code RS(73,81) [i]
- discarding factors / shortening the dual code based on linear OA(818, 81, F81, 8) (dual of [81, 73, 9]-code or 81-arc in PG(7,81)), 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(9150, 13174, F9, 34) (dual of [13174, 13024, 35]-code) | [i] | Trace Code | |
| 2 | Linear OOA(8175, 4126, F81, 2, 34) (dual of [(4126, 2), 8177, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(8175, 4126, F81, 3, 34) (dual of [(4126, 3), 12303, 35]-NRT-code) | [i] | ||
| 4 | Linear OOA(8175, 4126, F81, 4, 34) (dual of [(4126, 4), 16429, 35]-NRT-code) | [i] | ||
| 5 | Digital (41, 75, 4126)-net over F81 | [i] | ||
| 6 | Linear OOA(8175, 3293, F81, 2, 34) (dual of [(3293, 2), 6511, 35]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(8175, 2195, F81, 3, 34) (dual of [(2195, 3), 6510, 35]-NRT-code) | [i] | ||