Information on Result #1552031
Linear OOA(769, 16841, F7, 3, 15) (dual of [(16841, 3), 50454, 16]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(769, 16841, F7, 15) (dual of [16841, 16772, 16]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(768, 16839, F7, 15) (dual of [16839, 16771, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(8) [i] based on
- linear OA(761, 16807, F7, 15) (dual of [16807, 16746, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(736, 16807, F7, 9) (dual of [16807, 16771, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(77, 32, F7, 5) (dual of [32, 25, 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(768, 16840, F7, 14) (dual of [16840, 16772, 15]-code), using Gilbert–Varšamov bound and bm = 768 > Vbs−1(k−1) = 18 274332 684976 819635 107453 068386 991466 558295 990329 181943 [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(768, 16839, F7, 15) (dual of [16839, 16771, 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(769, 5613, F7, 21, 15) (dual of [(5613, 21), 117804, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |