Information on Result #684764
Linear OA(716, 16812, F7, 4) (dual of [16812, 16796, 5]-code), using construction X applied to Ce(3) ⊂ Ce(2) based on
- linear OA(716, 16807, F7, 4) (dual of [16807, 16791, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(711, 16807, F7, 3) (dual of [16807, 16796, 4]-code or 16807-cap in PG(10,7)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [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 OOA(716, 16812, F7, 2, 4) (dual of [(16812, 2), 33608, 5]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(716, 16812, F7, 3, 4) (dual of [(16812, 3), 50420, 5]-NRT-code) | [i] | ||
| 3 | Linear OOA(716, 8406, F7, 2, 4) (dual of [(8406, 2), 16796, 5]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(716, 8406, F7, 3, 4) (dual of [(8406, 3), 25202, 5]-NRT-code) | [i] | OA Folding and Stacking | |