Information on Result #1839146
OOA(12876, 8388600, S128, 4, 12), using discarding parts of the base based on linear OOA(25666, 8388600, F256, 4, 12) (dual of [(8388600, 4), 33554334, 13]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(2566, 2097150, F256, 4, 3) (dual of [(2097150, 4), 8388594, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2566, large, F256, 4, 3), using
- appending 1 arbitrary column [i] based on linear OOA(2566, large, F256, 3, 3), using
- appending kth column [i] based on linear OOA(2566, large, F256, 2, 3), using
- OAs with strength 3, b ≠ 2, and m > 3 are always embeddable [i] based on linear OA(2566, large, F256, 3) (dual of [large, large−6, 4]-code), using
- appending kth column [i] based on linear OOA(2566, large, F256, 2, 3), using
- appending 1 arbitrary column [i] based on linear OOA(2566, large, F256, 3, 3), using
- discarding factors / shortening the dual code based on linear OOA(2566, large, F256, 4, 3), using
- linear OOA(25610, 2097150, F256, 4, 4) (dual of [(2097150, 4), 8388590, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25610, 4194301, F256, 4, 4) (dual of [(4194301, 4), 16777194, 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, 4, 4) (dual of [(4194301, 4), 16777194, 5]-NRT-code), using
- linear OOA(25616, 2097150, F256, 4, 6) (dual of [(2097150, 4), 8388584, 7]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25616, 2796201, F256, 4, 6) (dual of [(2796201, 4), 11184788, 7]-NRT-code), using
- OA 3-folding and stacking [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]
- OA 3-folding and stacking [i] based on linear OA(25616, large, F256, 6) (dual of [large, large−16, 7]-code), using
- discarding factors / shortening the dual code based on linear OOA(25616, 2796201, F256, 4, 6) (dual of [(2796201, 4), 11184788, 7]-NRT-code), using
- linear OOA(25634, 2097150, F256, 4, 12) (dual of [(2097150, 4), 8388566, 13]-NRT-code), using
- OOA 4-folding [i] based on linear OA(25634, 8388600, F256, 12) (dual of [8388600, 8388566, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(25634, large, F256, 12) (dual of [large, large−34, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(25634, large, F256, 12) (dual of [large, large−34, 13]-code), using
- OOA 4-folding [i] based on linear OA(25634, 8388600, F256, 12) (dual of [8388600, 8388566, 13]-code), using
- linear OOA(2566, 2097150, F256, 4, 3) (dual of [(2097150, 4), 8388594, 4]-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(12877, 8388600, S128, 4, 12) | [i] | OOA Duplication | |