Information on Result #1022977
Linear OOA(25666, 5625171, F256, 3, 14) (dual of [(5625171, 3), 16875447, 15]-NRT-code), using generalized (u, u+v)-construction based on
- linear OOA(2567, 32769, F256, 3, 4) (dual of [(32769, 3), 98300, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(2567, 65538, F256, 4) (dual of [65538, 65531, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(2567, 65536, F256, 4) (dual of [65536, 65529, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(2565, 65536, F256, 3) (dual of [65536, 65531, 4]-code or 65536-cap in PG(4,256)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- OA 2-folding and stacking [i] based on linear OA(2567, 65538, F256, 4) (dual of [65538, 65531, 5]-code), using
- linear OOA(25619, 2796201, F256, 3, 7) (dual of [(2796201, 3), 8388584, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(25619, large, F256, 7) (dual of [large, large−19, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- OOA 3-folding [i] based on linear OA(25619, large, F256, 7) (dual of [large, large−19, 8]-code), using
- linear OOA(25640, 2796201, F256, 3, 14) (dual of [(2796201, 3), 8388563, 15]-NRT-code), using
- OOA 3-folding [i] based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- OOA 3-folding [i] based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | OOA(12876, 5625171, S128, 3, 14) | [i] | Discarding Parts of the Base for OOAs | |
| 2 | Linear OOA(25666, 2812585, F256, 5, 14) (dual of [(2812585, 5), 14062859, 15]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(25666, 2812585, F256, 6, 14) (dual of [(2812585, 6), 16875444, 15]-NRT-code) | [i] | ||