Information on Result #684598
Linear OA(755, 823570, F7, 9) (dual of [823570, 823515, 10]-code), using construction XX applied to Ce(8) ⊂ Ce(4) ⊂ Ce(3) based on
- linear OA(750, 823543, F7, 9) (dual of [823543, 823493, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(729, 823543, F7, 5) (dual of [823543, 823514, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(722, 823543, F7, 4) (dual of [823543, 823521, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(74, 26, F7, 3) (dual of [26, 22, 4]-code or 26-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(755, 823570, F7, 2, 9) (dual of [(823570, 2), 1647085, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(755, 823570, F7, 3, 9) (dual of [(823570, 3), 2470655, 10]-NRT-code) | [i] | ||
| 3 | Digital (46, 55, 823570)-net over F7 | [i] | ||
| 4 | Linear OOA(755, 411785, F7, 2, 9) (dual of [(411785, 2), 823515, 10]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(755, 274523, F7, 3, 9) (dual of [(274523, 3), 823514, 10]-NRT-code) | [i] | ||