Information on Result #1442102
Linear OOA(788, 117690, F7, 2, 16) (dual of [(117690, 2), 235292, 17]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(788, 117690, F7, 16) (dual of [117690, 117602, 17]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(786, 117686, F7, 16) (dual of [117686, 117600, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(9) [i] based on
- linear OA(779, 117649, F7, 16) (dual of [117649, 117570, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(749, 117649, F7, 10) (dual of [117649, 117600, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(15) ⊂ Ce(9) [i] based on
- linear OA(786, 117688, F7, 15) (dual of [117688, 117602, 16]-code), using Gilbert–Varšamov bound and bm = 786 > Vbs−1(k−1) = 87817 451724 636967 389692 410859 285688 681074 312109 236557 365406 878924 357751 [i]
- linear OA(70, 2, F7, 0) (dual of [2, 2, 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(786, 117686, F7, 16) (dual of [117686, 117600, 17]-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(788, 58845, F7, 3, 16) (dual of [(58845, 3), 176447, 17]-NRT-code) | [i] | OOA Folding | |