Information on Result #1441859
Linear OOA(781, 117688, F7, 2, 15) (dual of [(117688, 2), 235295, 16]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(781, 117688, F7, 15) (dual of [117688, 117607, 16]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(780, 117686, F7, 15) (dual of [117686, 117606, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(8) [i] based on
- 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(743, 117649, F7, 9) (dual of [117649, 117606, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(77, 37, F7, 5) (dual of [37, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code), using
- construction X applied to Ce(14) ⊂ Ce(8) [i] based on
- linear OA(780, 117687, F7, 14) (dual of [117687, 117607, 15]-code), using Gilbert–Varšamov bound and bm = 780 > Vbs−1(k−1) = 1 741119 215661 444466 630180 041120 390091 804502 401096 839311 961343 410193 [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(780, 117686, F7, 15) (dual of [117686, 117606, 16]-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(781, 58844, F7, 3, 15) (dual of [(58844, 3), 176451, 16]-NRT-code) | [i] | OOA Folding | |