Information on Result #1013892
Linear OOA(789, 1921619, F7, 3, 12) (dual of [(1921619, 3), 5764768, 13]-NRT-code), using (u, u+v)-construction based on
- linear OOA(77, 13, F7, 3, 6) (dual of [(13, 3), 32, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 7, 13)-net over F7, using
- 6 times m-reduction [i] based on digital (1, 13, 13)-net over F7, using
- extracting embedded OOA [i] based on digital (1, 7, 13)-net over F7, using
- linear OOA(782, 1921606, F7, 3, 12) (dual of [(1921606, 3), 5764736, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(782, 5764818, F7, 12) (dual of [5764818, 5764736, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- linear OA(781, 5764801, F7, 12) (dual of [5764801, 5764720, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(765, 5764801, F7, 10) (dual of [5764801, 5764736, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(71, 17, F7, 1) (dual of [17, 16, 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
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- OOA 3-folding [i] based on linear OA(782, 5764818, F7, 12) (dual of [5764818, 5764736, 13]-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, 960809, F7, 15, 12) (dual of [(960809, 15), 14412046, 13]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |