Information on Result #684596
Linear OA(762, 823570, F7, 10) (dual of [823570, 823508, 11]-code), using construction XX applied to Ce(9) ⊂ Ce(5) ⊂ Ce(4) based on
- linear OA(757, 823543, F7, 10) (dual of [823543, 823486, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(736, 823543, F7, 6) (dual of [823543, 823507, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(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(762, 823570, F7, 2, 10) (dual of [(823570, 2), 1647078, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(762, 823570, F7, 3, 10) (dual of [(823570, 3), 2470648, 11]-NRT-code) | [i] | ||
| 3 | Digital (52, 62, 823570)-net over F7 | [i] | ||
| 4 | Linear OOA(762, 411785, F7, 2, 10) (dual of [(411785, 2), 823508, 11]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(762, 274523, F7, 3, 10) (dual of [(274523, 3), 823507, 11]-NRT-code) | [i] | ||
| 6 | Linear OOA(762, 164714, F7, 10, 10) (dual of [(164714, 10), 1647078, 11]-NRT-code) | [i] | OA Folding and Stacking | |