Information on Result #1832565
OOA(12858, 32919, S128, 2, 21), using (u, u+v)-construction based on
- linear OOA(12811, 150, F128, 2, 10) (dual of [(150, 2), 289, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,289P) [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- OOA(12847, 32769, S128, 2, 21), using
- OOA 2-folding [i] based on OA(12847, 65538, S128, 21), using
- discarding parts of the base [i] based on linear OA(25641, 65538, F256, 21) (dual of [65538, 65497, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- linear OA(25641, 65536, F256, 21) (dual of [65536, 65495, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(25639, 65536, F256, 20) (dual of [65536, 65497, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- discarding parts of the base [i] based on linear OA(25641, 65538, F256, 21) (dual of [65538, 65497, 22]-code), using
- OOA 2-folding [i] based on OA(12847, 65538, S128, 21), using
Mode: Constructive.
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 | OOA(12858, 16459, S128, 4, 21) | [i] | OOA Folding | |
| 2 | OOA(12858, 6583, S128, 22, 21) | [i] | OOA Folding and Stacking with Additional Row | |