Information on Result #1071138
Linear OOA(12878, 4097, F128, 4, 39) (dual of [(4097, 4), 16310, 40]-NRT-code), using OOA 4-folding based on linear OA(12878, 16388, F128, 39) (dual of [16388, 16310, 40]-code), using
- discarding factors / shortening the dual code based on linear OA(12878, 16390, F128, 39) (dual of [16390, 16312, 40]-code), using
- construction X applied to C([0,19]) ⊂ C([0,18]) [i] based on
- linear OA(12877, 16385, F128, 39) (dual of [16385, 16308, 40]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,19], and minimum distance d ≥ |{−19,−18,…,19}|+1 = 40 (BCH-bound) [i]
- linear OA(12873, 16385, F128, 37) (dual of [16385, 16312, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (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([0,19]) ⊂ C([0,18]) [i] based on
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 | Digital (39, 78, 4095)-net over F128 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |