Information on Result #1836594
OOA(8149, 5636094, S8, 3, 15), using (u, u+v)-construction based on
- OOA(835, 43692, S8, 3, 7), using
- OOA 3-folding [i] based on OA(835, 131076, S8, 7), using
- discarding parts of the base [i] based on linear OA(1626, 131076, F16, 7) (dual of [131076, 131050, 8]-code), using
- trace code [i] based on linear OA(25613, 65538, F256, 7) (dual of [65538, 65525, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(25613, 65536, F256, 7) (dual of [65536, 65523, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(25611, 65536, F256, 6) (dual of [65536, 65525, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(6) ⊂ Ce(5) [i] based on
- trace code [i] based on linear OA(25613, 65538, F256, 7) (dual of [65538, 65525, 8]-code), using
- discarding parts of the base [i] based on linear OA(1626, 131076, F16, 7) (dual of [131076, 131050, 8]-code), using
- OOA 3-folding [i] based on OA(835, 131076, S8, 7), using
- linear OOA(8114, 5592402, F8, 3, 15) (dual of [(5592402, 3), 16777092, 16]-NRT-code), using
- trace code [i] based on linear OOA(6457, 2796201, F64, 3, 15) (dual of [(2796201, 3), 8388546, 16]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6457, large, F64, 15) (dual of [large, large−57, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(6457, large, F64, 15) (dual of [large, large−57, 16]-code), using
- trace code [i] based on linear OOA(6457, 2796201, F64, 3, 15) (dual of [(2796201, 3), 8388546, 16]-NRT-code), using
Mode: Constructive.
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(8150, 5636094, S8, 3, 15) | [i] | OOA Duplication | |