Information on Result #735619
Linear OA(12858, 16580, F128, 22) (dual of [16580, 16522, 23]-code), using (u, u+v)-construction based on
- linear OA(12815, 194, F128, 11) (dual of [194, 179, 12]-code), using
- construction X applied to AG(F,179P) ⊂ AG(F,181P) [i] based on
- linear OA(12814, 191, F128, 11) (dual of [191, 177, 12]-code), using algebraic-geometric code AG(F,179P) [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- linear OA(12812, 191, F128, 9) (dual of [191, 179, 10]-code), using algebraic-geometric code AG(F,181P) [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,179P) ⊂ AG(F,181P) [i] based on
- linear OA(12843, 16386, F128, 22) (dual of [16386, 16343, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(12843, 16384, F128, 22) (dual of [16384, 16341, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(12841, 16384, F128, 21) (dual of [16384, 16343, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(21) ⊂ Ce(20) [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(12858, 8290, F128, 2, 22) (dual of [(8290, 2), 16522, 23]-NRT-code) | [i] | OOA Folding | |