Information on Result #684789
Linear OA(734, 16820, F7, 8) (dual of [16820, 16786, 9]-code), using construction X applied to Ce(7) ⊂ Ce(4) based on
- linear OA(731, 16807, F7, 8) (dual of [16807, 16776, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(73, 13, F7, 2) (dual of [13, 10, 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(734, 16820, F7, 2, 8) (dual of [(16820, 2), 33606, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(734, 16820, F7, 3, 8) (dual of [(16820, 3), 50426, 9]-NRT-code) | [i] | ||
| 3 | Digital (26, 34, 16820)-net over F7 | [i] | ||
| 4 | Linear OOA(734, 8410, F7, 2, 8) (dual of [(8410, 2), 16786, 9]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(734, 5606, F7, 3, 8) (dual of [(5606, 3), 16784, 9]-NRT-code) | [i] | ||
| 6 | Linear OOA(734, 4205, F7, 8, 8) (dual of [(4205, 8), 33606, 9]-NRT-code) | [i] | OA Folding and Stacking | |