Information on Result #1014234
Linear OOA(841, 174773, F8, 3, 7) (dual of [(174773, 3), 524278, 8]-NRT-code), using (u, u+v)-construction based on
- linear OOA(83, 9, F8, 3, 3) (dual of [(9, 3), 24, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;24,8) [i]
- linear OOA(838, 174764, F8, 3, 7) (dual of [(174764, 3), 524254, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(838, 524292, F8, 7) (dual of [524292, 524254, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(838, 524294, F8, 7) (dual of [524294, 524256, 8]-code), using
- trace code [i] based on linear OA(6419, 262147, F64, 7) (dual of [262147, 262128, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(6419, 262144, F64, 7) (dual of [262144, 262125, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(6416, 262144, F64, 6) (dual of [262144, 262128, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- trace code [i] based on linear OA(6419, 262147, F64, 7) (dual of [262147, 262128, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(838, 524294, F8, 7) (dual of [524294, 524256, 8]-code), using
- OOA 3-folding [i] based on linear OA(838, 524292, F8, 7) (dual of [524292, 524254, 8]-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(8147, 5767175, F8, 3, 14) (dual of [(5767175, 3), 17301378, 15]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(8155, 5767175, F8, 3, 15) (dual of [(5767175, 3), 17301370, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(841, 174772, F8, 9, 7) (dual of [(174772, 9), 1572907, 8]-NRT-code) | [i] | OOA Stacking with Additional Row | |