Information on Result #1837649
OOA(12872, large, S128, 3, 13), using discarding parts of the base based on linear OOA(25663, large, F256, 3, 13), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(25610, 2796201, F256, 3, 4) (dual of [(2796201, 3), 8388593, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25610, 4194301, F256, 3, 4) (dual of [(4194301, 3), 12582893, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(25610, 8388602, F256, 4) (dual of [8388602, 8388592, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(25610, large, F256, 4) (dual of [large, large−10, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(25610, large, F256, 4) (dual of [large, large−10, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(25610, 8388602, F256, 4) (dual of [8388602, 8388592, 5]-code), using
- discarding factors / shortening the dual code based on linear OOA(25610, 4194301, F256, 3, 4) (dual of [(4194301, 3), 12582893, 5]-NRT-code), using
- linear OOA(25616, 2796201, F256, 3, 6) (dual of [(2796201, 3), 8388587, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(25616, large, F256, 6) (dual of [large, large−16, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OOA 3-folding [i] based on linear OA(25616, large, F256, 6) (dual of [large, large−16, 7]-code), using
- linear OOA(25637, 2796201, F256, 3, 13) (dual of [(2796201, 3), 8388566, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(25637, large, F256, 13) (dual of [large, large−37, 14]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- OOA 3-folding [i] based on linear OA(25637, large, F256, 13) (dual of [large, large−37, 14]-code), using
- linear OOA(25610, 2796201, F256, 3, 4) (dual of [(2796201, 3), 8388593, 5]-NRT-code), using
Mode: Constructive.
Optimality
Show details for fixed k and m, k and t, 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(12872, large, S128, 3, 12) | [i] | Strength Reduction for OOAs | |
| 2 | OOA(12875, large, S128, 3, 13) | [i] | NRT-Code Embedding in Larger Space | |
| 3 | OOA(12878, large, S128, 3, 13) | [i] | ||
| 4 | OOA(12873, large, S128, 3, 13) | [i] | OOA Duplication | |
| 5 | OOA(12874, large, S128, 3, 13) | [i] | ||