Information on Result #1443054
Linear OOA(7110, 117687, F7, 2, 20) (dual of [(117687, 2), 235264, 21]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(7110, 117687, F7, 20) (dual of [117687, 117577, 21]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(7109, 117685, F7, 20) (dual of [117685, 117576, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(14) [i] based on
- linear OA(7103, 117649, F7, 20) (dual of [117649, 117546, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(773, 117649, F7, 15) (dual of [117649, 117576, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(76, 36, F7, 4) (dual of [36, 30, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(76, 42, F7, 4) (dual of [42, 36, 5]-code), using
- 1 times truncation [i] based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(76, 42, F7, 4) (dual of [42, 36, 5]-code), using
- construction X applied to Ce(19) ⊂ Ce(14) [i] based on
- linear OA(7109, 117686, F7, 19) (dual of [117686, 117577, 20]-code), using Gilbert–Varšamov bound and bm = 7109 > Vbs−1(k−1) = 297035 203695 390481 730521 950909 199848 769024 085162 480714 965181 872598 389150 920975 593554 151719 [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(7109, 117685, F7, 20) (dual of [117685, 117576, 21]-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(7110, 58843, F7, 3, 20) (dual of [(58843, 3), 176419, 21]-NRT-code) | [i] | OOA Folding | |