Information on Result #1302166
Linear OA(774, 16822, F7, 17) (dual of [16822, 16748, 18]-code), using construction X with Varšamov bound based on
- linear OA(772, 16819, F7, 17) (dual of [16819, 16747, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,7]) [i] based on
- 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(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(71, 11, F7, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,8]) ⊂ C([0,7]) [i] based on
- linear OA(772, 16820, F7, 15) (dual of [16820, 16748, 16]-code), using Gilbert–Varšamov bound and bm = 772 > Vbs−1(k−1) = 129604 906208 624288 167871 316980 443286 718659 294936 785622 946007 [i]
- linear OA(71, 2, F7, 1) (dual of [2, 1, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (see above)
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(774, 8411, F7, 2, 17) (dual of [(8411, 2), 16748, 18]-NRT-code) | [i] | OOA Folding | |