Information on Result #1552557
Linear OOA(786, 16834, F7, 3, 19) (dual of [(16834, 3), 50416, 20]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(786, 16834, F7, 19) (dual of [16834, 16748, 20]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(785, 16832, F7, 19) (dual of [16832, 16747, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,7]) [i] based on
- linear OA(781, 16808, F7, 19) (dual of [16808, 16727, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 16808 | 710−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(761, 16808, F7, 15) (dual of [16808, 16747, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 16808 | 710−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(74, 24, F7, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,7)), using
- construction X applied to C([0,9]) ⊂ C([0,7]) [i] based on
- linear OA(785, 16833, F7, 18) (dual of [16833, 16748, 19]-code), using Gilbert–Varšamov bound and bm = 785 > Vbs−1(k−1) = 32989 294105 206223 001405 174883 080732 242307 607219 744237 045160 634340 751873 [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(785, 16832, F7, 19) (dual of [16832, 16747, 20]-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(786, 5611, F7, 21, 19) (dual of [(5611, 21), 117745, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |