Information on Result #905042
Linear OOA(12843, 8345, F128, 2, 17) (dual of [(8345, 2), 16647, 18]-NRT-code), using (u, u+v)-construction based on
- linear OOA(1289, 150, F128, 2, 8) (dual of [(150, 2), 291, 9]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,291P) [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- linear OOA(12834, 8195, F128, 2, 17) (dual of [(8195, 2), 16356, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12834, 16390, F128, 17) (dual of [16390, 16356, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,7]) [i] based on
- linear OA(12833, 16385, F128, 17) (dual of [16385, 16352, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(12829, 16385, F128, 15) (dual of [16385, 16356, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (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([0,8]) ⊂ C([0,7]) [i] based on
- OOA 2-folding [i] based on linear OA(12834, 16390, F128, 17) (dual of [16390, 16356, 18]-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(12843, 4172, F128, 4, 17) (dual of [(4172, 4), 16645, 18]-NRT-code) | [i] | OOA Folding | |