Information on Result #735707
Linear OA(12847, 16578, F128, 18) (dual of [16578, 16531, 19]-code), using (u, u+v)-construction based on
- linear OA(12812, 192, F128, 9) (dual of [192, 180, 10]-code), using
- extended algebraic-geometric code AGe(F,182P) [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- linear OA(12835, 16386, F128, 18) (dual of [16386, 16351, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(12835, 16384, F128, 18) (dual of [16384, 16349, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(12833, 16384, F128, 17) (dual of [16384, 16351, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(17) ⊂ Ce(16) [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(12847, 8289, F128, 2, 18) (dual of [(8289, 2), 16531, 19]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(12847, 5526, F128, 3, 18) (dual of [(5526, 3), 16531, 19]-NRT-code) | [i] | ||