Information on Result #735661
Linear OA(12853, 16580, F128, 20) (dual of [16580, 16527, 21]-code), using (u, u+v)-construction based on
- linear OA(12814, 194, F128, 10) (dual of [194, 180, 11]-code), using
- construction X applied to AG(F,180P) ⊂ AG(F,182P) [i] based on
- linear OA(12813, 191, F128, 10) (dual of [191, 178, 11]-code), using algebraic-geometric code AG(F,180P) [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- linear OA(12811, 191, F128, 8) (dual of [191, 180, 9]-code), using algebraic-geometric code AG(F,182P) [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192 (see above)
- linear OA(1281, 3, F128, 1) (dual of [3, 2, 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 AG(F,180P) ⊂ AG(F,182P) [i] based on
- linear OA(12839, 16386, F128, 20) (dual of [16386, 16347, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(12839, 16384, F128, 20) (dual of [16384, 16345, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(12837, 16384, F128, 19) (dual of [16384, 16347, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(19) ⊂ Ce(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 | Linear OOA(12853, 8290, F128, 2, 20) (dual of [(8290, 2), 16527, 21]-NRT-code) | [i] | OOA Folding | |