Information on Result #1085161
Linear OOA(25657, 4227069, F256, 4, 12) (dual of [(4227069, 4), 16908219, 13]-NRT-code), using generalized (u, u+v)-construction based on
- linear OOA(2567, 32769, F256, 4, 4) (dual of [(32769, 4), 131069, 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(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
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(12866, 4227069, S128, 4, 12) | [i] | Discarding Parts of the Base for OOAs | |