Information on Result #1442063
Linear OOA(787, 16836, F7, 2, 19) (dual of [(16836, 2), 33585, 20]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(787, 16836, F7, 19) (dual of [16836, 16749, 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, 16834, F7, 18) (dual of [16834, 16749, 19]-code), using Gilbert–Varšamov bound and bm = 785 > Vbs−1(k−1) = 33022 644035 944578 737604 669925 932623 500856 326173 954353 309853 770414 790151 [i]
- linear OA(70, 2, F7, 0) (dual of [2, 2, 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(787, 8418, F7, 3, 19) (dual of [(8418, 3), 25167, 20]-NRT-code) | [i] | OOA Folding | |