Information on Result #684800
Linear OA(784, 16825, F7, 19) (dual of [16825, 16741, 20]-code), using construction X applied to Ce(18) ⊂ Ce(15) based on
- linear OA(781, 16807, F7, 19) (dual of [16807, 16726, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 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(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(784, 15980, F7, 2, 19) (dual of [(15980, 2), 31876, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(784, 15980, F7, 3, 19) (dual of [(15980, 3), 47856, 20]-NRT-code) | [i] | ||
| 3 | Digital (65, 84, 15980)-net over F7 | [i] | ||
| 4 | Linear OOA(784, 8412, F7, 2, 19) (dual of [(8412, 2), 16740, 20]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(784, 5608, F7, 3, 19) (dual of [(5608, 3), 16740, 20]-NRT-code) | [i] | ||
| 6 | Linear OOA(784, 1869, F7, 19, 19) (dual of [(1869, 19), 35427, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |