Information on Result #905676
Linear OOA(25657, 4227072, F256, 2, 15) (dual of [(4227072, 2), 8454087, 16]-NRT-code), using (u, u+v)-construction based on
- linear OOA(25614, 32771, F256, 2, 7) (dual of [(32771, 2), 65528, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25614, 65542, F256, 7) (dual of [65542, 65528, 8]-code), using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
- linear OA(25613, 65537, F256, 7) (dual of [65537, 65524, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(2569, 65537, F256, 5) (dual of [65537, 65528, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
- OOA 2-folding [i] based on linear OA(25614, 65542, F256, 7) (dual of [65542, 65528, 8]-code), using
- linear OOA(25643, 4194301, F256, 2, 15) (dual of [(4194301, 2), 8388559, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25643, 8388602, F256, 15) (dual of [8388602, 8388559, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(25643, large, F256, 15) (dual of [large, large−43, 16]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(25643, large, F256, 15) (dual of [large, large−43, 16]-code), using
- OOA 2-folding [i] based on linear OA(25643, 8388602, F256, 15) (dual of [8388602, 8388559, 16]-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(25657, 2113536, F256, 4, 15) (dual of [(2113536, 4), 8454087, 16]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(25657, 1409024, F256, 6, 15) (dual of [(1409024, 6), 8454087, 16]-NRT-code) | [i] | ||