Information on Result #684784
Linear OA(742, 16818, F7, 10) (dual of [16818, 16776, 11]-code), using construction X applied to Ce(9) ⊂ Ce(7) based on
- linear OA(741, 16807, F7, 10) (dual of [16807, 16766, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- 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(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(742, 13444, F7, 2, 10) (dual of [(13444, 2), 26846, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(742, 13444, F7, 3, 10) (dual of [(13444, 3), 40290, 11]-NRT-code) | [i] | ||
| 3 | Digital (32, 42, 13444)-net over F7 | [i] | ||
| 4 | Linear OOA(742, 8409, F7, 2, 10) (dual of [(8409, 2), 16776, 11]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(742, 5606, F7, 3, 10) (dual of [(5606, 3), 16776, 11]-NRT-code) | [i] | ||
| 6 | Linear OOA(742, 3363, F7, 10, 10) (dual of [(3363, 10), 33588, 11]-NRT-code) | [i] | OA Folding and Stacking | |