Information on Result #684502
Linear OA(754, 5764831, F7, 8) (dual of [5764831, 5764777, 9]-code), using construction XX applied to Ce(7) ⊂ Ce(3) ⊂ Ce(2) based on
- linear OA(749, 5764801, F7, 8) (dual of [5764801, 5764752, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(725, 5764801, F7, 4) (dual of [5764801, 5764776, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(717, 5764801, F7, 3) (dual of [5764801, 5764784, 4]-code or 5764801-cap in PG(16,7)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(74, 29, F7, 3) (dual of [29, 25, 4]-code or 29-cap in PG(3,7)), using
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
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 OOA(754, 5764831, F7, 2, 8) (dual of [(5764831, 2), 11529608, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(754, 5764831, F7, 3, 8) (dual of [(5764831, 3), 17294439, 9]-NRT-code) | [i] | ||
| 3 | Digital (46, 54, 5764831)-net over F7 | [i] | ||
| 4 | Linear OOA(754, 2882415, F7, 2, 8) (dual of [(2882415, 2), 5764776, 9]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(754, 1921610, F7, 3, 8) (dual of [(1921610, 3), 5764776, 9]-NRT-code) | [i] | ||