Information on Result #684799
Linear OA(789, 16825, F7, 20) (dual of [16825, 16736, 21]-code), using construction X applied to Ce(19) ⊂ Ce(16) 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(771, 16807, F7, 17) (dual of [16807, 16736, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(73, 18, F7, 2) (dual of [18, 15, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(73, 48, F7, 2) (dual of [48, 45, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(73, 48, F7, 2) (dual of [48, 45, 3]-code), 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(789, 16825, F7, 2, 20) (dual of [(16825, 2), 33561, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(789, 16825, F7, 3, 20) (dual of [(16825, 3), 50386, 21]-NRT-code) | [i] | ||
| 3 | Digital (69, 89, 16825)-net over F7 | [i] | ||
| 4 | Linear OOA(789, 8412, F7, 2, 20) (dual of [(8412, 2), 16735, 21]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(789, 5608, F7, 3, 20) (dual of [(5608, 3), 16735, 21]-NRT-code) | [i] | ||