Information on Result #735506
Linear OA(12878, 16540, F128, 31) (dual of [16540, 16462, 32]-code), using (u, u+v)-construction based on
- linear OA(12816, 150, F128, 15) (dual of [150, 134, 16]-code), using
- extended algebraic-geometric code AGe(F,134P) [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- linear OA(12862, 16390, F128, 31) (dual of [16390, 16328, 32]-code), using
- construction X applied to C([0,15]) ⊂ C([0,14]) [i] based on
- linear OA(12861, 16385, F128, 31) (dual of [16385, 16324, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(12857, 16385, F128, 29) (dual of [16385, 16328, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (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([0,15]) ⊂ C([0,14]) [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 | Linear OOA(12878, 8270, F128, 2, 31) (dual of [(8270, 2), 16462, 32]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(12878, 5513, F128, 3, 31) (dual of [(5513, 3), 16461, 32]-NRT-code) | [i] | ||