Information on Result #735529
Linear OA(12873, 16580, F128, 28) (dual of [16580, 16507, 29]-code), using (u, u+v)-construction based on
- linear OA(12818, 194, F128, 14) (dual of [194, 176, 15]-code), using
- construction X applied to AG(F,176P) ⊂ AG(F,178P) [i] based on
- linear OA(12817, 191, F128, 14) (dual of [191, 174, 15]-code), using algebraic-geometric code AG(F,176P) [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- linear OA(12815, 191, F128, 12) (dual of [191, 176, 13]-code), using algebraic-geometric code AG(F,178P) [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,176P) ⊂ AG(F,178P) [i] based on
- linear OA(12855, 16386, F128, 28) (dual of [16386, 16331, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(26) [i] based on
- linear OA(12855, 16384, F128, 28) (dual of [16384, 16329, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(12853, 16384, F128, 27) (dual of [16384, 16331, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [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(27) ⊂ Ce(26) [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(12873, 8290, F128, 2, 28) (dual of [(8290, 2), 16507, 29]-NRT-code) | [i] | OOA Folding | |