Information on Result #1552146
Linear OOA(773, 823561, F7, 3, 12) (dual of [(823561, 3), 2470610, 13]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(773, 823561, F7, 12) (dual of [823561, 823488, 13]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(772, 823559, F7, 12) (dual of [823559, 823487, 13]-code), using
- construction X4 applied to Ce(11) ⊂ Ce(9) [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(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(715, 16, F7, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,7)), using
- dual of repetition code with length 16 [i]
- linear OA(71, 16, F7, 1) (dual of [16, 15, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, 342, F7, 1) (dual of [342, 341, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(71, 342, F7, 1) (dual of [342, 341, 2]-code), using
- construction X4 applied to Ce(11) ⊂ Ce(9) [i] based on
- linear OA(772, 823560, F7, 11) (dual of [823560, 823488, 12]-code), using Gilbert–Varšamov bound and bm = 772 > Vbs−1(k−1) = 2 391518 779504 139374 297788 919597 266944 778868 777595 476355 021047 [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(772, 823559, F7, 12) (dual of [823559, 823487, 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(773, 411780, F7, 15, 12) (dual of [(411780, 15), 6176627, 13]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |