Information on Result #1552596
Linear OOA(787, 117688, F7, 3, 16) (dual of [(117688, 3), 352977, 17]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(787, 117688, F7, 16) (dual of [117688, 117601, 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, 117687, F7, 15) (dual of [117687, 117601, 16]-code), using Gilbert–Varšamov bound and bm = 786 > Vbs−1(k−1) = 87807 005009 342998 722892 629779 038966 340523 485094 829976 329535 110863 896593 [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(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(787, 39229, F7, 21, 16) (dual of [(39229, 21), 823722, 17]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |