Information on Result #684761
Linear OA(726, 16812, F7, 6) (dual of [16812, 16786, 7]-code), using construction X applied to Ce(5) ⊂ Ce(4) based on
- linear OA(726, 16807, F7, 6) (dual of [16807, 16781, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(721, 16807, F7, 5) (dual of [16807, 16786, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(70, 5, F7, 0) (dual of [5, 5, 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
Mode: Constructive and 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 OA(730, 16862, F7, 6) (dual of [16862, 16832, 7]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OOA(726, 16812, F7, 2, 6) (dual of [(16812, 2), 33598, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(726, 16812, F7, 3, 6) (dual of [(16812, 3), 50410, 7]-NRT-code) | [i] | ||
| 4 | Digital (20, 26, 16812)-net over F7 | [i] | ||
| 5 | Linear OOA(726, 8406, F7, 2, 6) (dual of [(8406, 2), 16786, 7]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(726, 5604, F7, 3, 6) (dual of [(5604, 3), 16786, 7]-NRT-code) | [i] | ||
| 7 | Linear OOA(726, 5604, F7, 6, 6) (dual of [(5604, 6), 33598, 7]-NRT-code) | [i] | OA Folding and Stacking | |