Information on Result #1441640
Linear OOA(774, 16841, F7, 2, 16) (dual of [(16841, 2), 33608, 17]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(774, 16841, F7, 16) (dual of [16841, 16767, 17]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(773, 16839, F7, 16) (dual of [16839, 16766, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(9) [i] based on
- linear OA(766, 16807, F7, 16) (dual of [16807, 16741, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(741, 16807, F7, 10) (dual of [16807, 16766, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(15) ⊂ Ce(9) [i] based on
- linear OA(773, 16840, F7, 15) (dual of [16840, 16767, 16]-code), using Gilbert–Varšamov bound and bm = 773 > Vbs−1(k−1) = 131780 130096 442083 399015 830170 778250 345493 879350 105487 345399 [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(773, 16839, F7, 16) (dual of [16839, 16766, 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(774, 8420, F7, 3, 16) (dual of [(8420, 3), 25186, 17]-NRT-code) | [i] | OOA Folding | |