Information on Result #1019063
Linear OOA(12818, 10926, F128, 3, 7) (dual of [(10926, 3), 32760, 8]-NRT-code), using (u, u+v)-construction based on
- linear OOA(1284, 16385, F128, 3, 3) (dual of [(16385, 3), 49151, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(1284, 16385, F128, 2, 3) (dual of [(16385, 2), 32766, 4]-NRT-code), using
- linear OOA(12814, 5463, F128, 3, 7) (dual of [(5463, 3), 16375, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12814, 16389, F128, 7) (dual of [16389, 16375, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(12814, 16390, F128, 7) (dual of [16390, 16376, 8]-code), using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
- linear OA(12813, 16385, F128, 7) (dual of [16385, 16372, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(1289, 16385, F128, 5) (dual of [16385, 16376, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(1281, 5, F128, 1) (dual of [5, 4, 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([0,3]) ⊂ C([0,2]) [i] based on
- discarding factors / shortening the dual code based on linear OA(12814, 16390, F128, 7) (dual of [16390, 16376, 8]-code), using
- OOA 3-folding [i] based on linear OA(12814, 16389, F128, 7) (dual of [16389, 16375, 8]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n 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(12871, 2807127, F128, 3, 14) (dual of [(2807127, 3), 8421310, 15]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(12875, 2807127, F128, 3, 15) (dual of [(2807127, 3), 8421306, 16]-NRT-code) | [i] | ||