Information on Result #1302288
Linear OA(796, 16834, F7, 21) (dual of [16834, 16738, 22]-code), using construction X with Varšamov bound based on
- linear OA(795, 16832, F7, 21) (dual of [16832, 16737, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(791, 16808, F7, 21) (dual of [16808, 16717, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 16808 | 710−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(771, 16808, F7, 17) (dual of [16808, 16737, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16808 | 710−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (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([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(795, 16833, F7, 20) (dual of [16833, 16738, 21]-code), using Gilbert–Varšamov bound and bm = 795 > Vbs−1(k−1) = 981806 611056 746171 610126 210258 765796 223824 482297 991165 890147 907918 807133 993473 [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
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(796, 16834, F7, 2, 21) (dual of [(16834, 2), 33572, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(796, 16834, F7, 3, 21) (dual of [(16834, 3), 50406, 22]-NRT-code) | [i] | ||
| 3 | Digital (75, 96, 16834)-net over F7 | [i] | ||
| 4 | Linear OOA(796, 8417, F7, 2, 21) (dual of [(8417, 2), 16738, 22]-NRT-code) | [i] | OOA Folding | |