Information on Result #1832394
OOA(12846, 5242881, S128, 2, 10), using (u, u+v)-construction based on
- linear OOA(12814, 1048580, F128, 2, 5) (dual of [(1048580, 2), 2097146, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12814, 2097160, F128, 5) (dual of [2097160, 2097146, 6]-code), using
- construction X applied to C([0,2]) ⊂ C([0,1]) [i] based on
- linear OA(12813, 2097153, F128, 5) (dual of [2097153, 2097140, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(1287, 2097153, F128, 3) (dual of [2097153, 2097146, 4]-code or 2097153-cap in PG(6,128)), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,1], and minimum distance d ≥ |{−1,0,1}|+1 = 4 (BCH-bound) [i]
- linear OA(1281, 7, F128, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,2]) ⊂ C([0,1]) [i] based on
- OOA 2-folding [i] based on linear OA(12814, 2097160, F128, 5) (dual of [2097160, 2097146, 6]-code), using
- OOA(12832, 4194301, S128, 2, 10), using
- OOA 2-folding [i] based on OA(12832, 8388602, S128, 10), using
- discarding factors based on OA(12832, large, S128, 10), using
- discarding parts of the base [i] based on linear OA(25628, large, F256, 10) (dual of [large, large−28, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding parts of the base [i] based on linear OA(25628, large, F256, 10) (dual of [large, large−28, 11]-code), using
- discarding factors based on OA(12832, large, S128, 10), using
- OOA 2-folding [i] based on OA(12832, 8388602, S128, 10), 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(12846, 2621440, S128, 4, 10) | [i] | OOA Folding | |