Information on Result #684599
Linear OA(748, 823570, F7, 8) (dual of [823570, 823522, 9]-code), using construction XX applied to Ce(7) ⊂ Ce(3) ⊂ Ce(2) based on
- linear OA(743, 823543, F7, 8) (dual of [823543, 823500, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(715, 823543, F7, 3) (dual of [823543, 823528, 4]-code or 823543-cap in PG(14,7)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [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(748, 823570, F7, 2, 8) (dual of [(823570, 2), 1647092, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(748, 823570, F7, 3, 8) (dual of [(823570, 3), 2470662, 9]-NRT-code) | [i] | ||
| 3 | Digital (40, 48, 823570)-net over F7 | [i] | ||
| 4 | Linear OOA(748, 411785, F7, 2, 8) (dual of [(411785, 2), 823522, 9]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(748, 274523, F7, 3, 8) (dual of [(274523, 3), 823521, 9]-NRT-code) | [i] | ||