Information on Result #684773
Linear OA(787, 16818, F7, 20) (dual of [16818, 16731, 21]-code), using construction X applied to Ce(19) ⊂ Ce(17) based on
- linear OA(786, 16807, F7, 20) (dual of [16807, 16721, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(776, 16807, F7, 18) (dual of [16807, 16731, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(71, 11, F7, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-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(787, 13719, F7, 2, 20) (dual of [(13719, 2), 27351, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(787, 13719, F7, 3, 20) (dual of [(13719, 3), 41070, 21]-NRT-code) | [i] | ||
| 3 | Digital (67, 87, 13719)-net over F7 | [i] | ||
| 4 | Linear OOA(787, 8409, F7, 2, 20) (dual of [(8409, 2), 16731, 21]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(787, 5606, F7, 3, 20) (dual of [(5606, 3), 16731, 21]-NRT-code) | [i] | ||