Information on Result #1145553
Linear OOA(25666, 4194557, F256, 6, 13) (dual of [(4194557, 6), 25167276, 14]-NRT-code), using generalized (u, u+v)-construction based on
- linear OOA(2563, 257, F256, 6, 3) (dual of [(257, 6), 1539, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(6;1539,256) [i]
- linear OOA(25610, 1398100, F256, 6, 4) (dual of [(1398100, 6), 8388590, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25610, 4194300, F256, 6, 4) (dual of [(4194300, 6), 25165790, 5]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(25610, 4194301, F256, 2, 4) (dual of [(4194301, 2), 8388592, 5]-NRT-code), using
- OOA 2-folding [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
- OOA 2-folding [i] based on linear OA(25610, 8388602, F256, 4) (dual of [8388602, 8388592, 5]-code), using
- OOA stacking with additional row [i] based on linear OOA(25610, 4194301, F256, 2, 4) (dual of [(4194301, 2), 8388592, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25610, 4194300, F256, 6, 4) (dual of [(4194300, 6), 25165790, 5]-NRT-code), using
- linear OOA(25616, 1398100, F256, 6, 6) (dual of [(1398100, 6), 8388584, 7]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25616, 2796201, F256, 6, 6) (dual of [(2796201, 6), 16777190, 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, 6, 6) (dual of [(2796201, 6), 16777190, 7]-NRT-code), using
- linear OOA(25637, 1398100, F256, 6, 13) (dual of [(1398100, 6), 8388563, 14]-NRT-code), using
- OOA 6-folding [i] based on linear OA(25637, 8388600, F256, 13) (dual of [8388600, 8388563, 14]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(25637, large, F256, 13) (dual of [large, large−37, 14]-code), using
- OOA 6-folding [i] based on linear OA(25637, 8388600, F256, 13) (dual of [8388600, 8388563, 14]-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 | Linear OOA(25666, 4194556, F256, 18, 13) (dual of [(4194556, 18), 75501942, 14]-NRT-code) | [i] | OOA Stacking with Additional Row | |