Information on Result #684574
Linear OA(782, 823575, F7, 13) (dual of [823575, 823493, 14]-code), using construction X applied to Ce(12) ⊂ Ce(8) based on
- linear OA(778, 823543, F7, 13) (dual of [823543, 823465, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- 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(74, 32, F7, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,7)), 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(783, 823576, F7, 13) (dual of [823576, 823493, 14]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(782, 823575, F7, 2, 13) (dual of [(823575, 2), 1647068, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(782, 823575, F7, 3, 13) (dual of [(823575, 3), 2470643, 14]-NRT-code) | [i] | ||
| 4 | Digital (69, 82, 823575)-net over F7 | [i] | ||
| 5 | Linear OA(783, 823577, F7, 13) (dual of [823577, 823494, 14]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(782, 411787, F7, 2, 13) (dual of [(411787, 2), 823492, 14]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(782, 274525, F7, 3, 13) (dual of [(274525, 3), 823493, 14]-NRT-code) | [i] | ||
| 8 | Linear OOA(782, 137262, F7, 13, 13) (dual of [(137262, 13), 1784324, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |