Information on Result #1014022
Linear OOA(790, 5625, F7, 3, 18) (dual of [(5625, 3), 16785, 19]-NRT-code), using (u, u+v)-construction based on
- linear OOA(714, 21, F7, 3, 9) (dual of [(21, 3), 49, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(74, 8, F7, 3, 4) (dual of [(8, 3), 20, 5]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;20,7) [i]
- linear OOA(710, 13, F7, 3, 9) (dual of [(13, 3), 29, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 10, 13)-net over F7, using
- 3 times m-reduction [i] based on digital (1, 13, 13)-net over F7, using
- extracting embedded OOA [i] based on digital (1, 10, 13)-net over F7, using
- linear OOA(74, 8, F7, 3, 4) (dual of [(8, 3), 20, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(776, 5604, F7, 3, 18) (dual of [(5604, 3), 16736, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(776, 16812, F7, 18) (dual of [16812, 16736, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(776, 16807, F7, 18) (dual of [16807, 16731, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(70, 5, F7, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- OOA 3-folding [i] based on linear OA(776, 16812, F7, 18) (dual of [16812, 16736, 19]-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(790, 1874, F7, 21, 18) (dual of [(1874, 21), 39264, 19]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |