Information on Result #1441702
Linear OOA(776, 823577, F7, 2, 12) (dual of [(823577, 2), 1647078, 13]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(776, 823577, F7, 12) (dual of [823577, 823501, 13]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(775, 823575, F7, 12) (dual of [823575, 823500, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(7) [i] based on
- linear OA(771, 823543, F7, 12) (dual of [823543, 823472, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- 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(74, 32, F7, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,7)), using
- construction X applied to Ce(11) ⊂ Ce(7) [i] based on
- linear OA(775, 823576, F7, 11) (dual of [823576, 823501, 12]-code), using Gilbert–Varšamov bound and bm = 775 > Vbs−1(k−1) = 2 391983 443812 231727 974513 676006 148160 784098 101020 730361 028471 [i]
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(775, 823575, F7, 12) (dual of [823575, 823500, 13]-code), using
Mode: 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(776, 411788, F7, 3, 12) (dual of [(411788, 3), 1235288, 13]-NRT-code) | [i] | OOA Folding | |