Information on Result #1013666
Linear OOA(729, 5612, F7, 3, 6) (dual of [(5612, 3), 16807, 7]-NRT-code), using (u, u+v)-construction based on
- linear OOA(73, 8, F7, 3, 3) (dual of [(8, 3), 21, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;21,7) [i]
- linear OOA(726, 5604, F7, 3, 6) (dual of [(5604, 3), 16786, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(726, 16812, F7, 6) (dual of [16812, 16786, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(726, 16807, F7, 6) (dual of [16807, 16781, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(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(5) ⊂ Ce(4) [i] based on
- OOA 3-folding [i] based on linear OA(726, 16812, F7, 6) (dual of [16812, 16786, 7]-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(729, 5611, F7, 9, 6) (dual of [(5611, 9), 50470, 7]-NRT-code) | [i] | OOA Stacking with Additional Row | |