Information on Result #905165
Linear OOA(12876, 1048727, F128, 2, 22) (dual of [(1048727, 2), 2097378, 23]-NRT-code), using (u, u+v)-construction based on
- linear OOA(12812, 150, F128, 2, 11) (dual of [(150, 2), 288, 12]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,288P) [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- linear OOA(12864, 1048577, F128, 2, 22) (dual of [(1048577, 2), 2097090, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12864, 2097154, F128, 22) (dual of [2097154, 2097090, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(12864, 2097155, F128, 22) (dual of [2097155, 2097091, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(12864, 2097152, F128, 22) (dual of [2097152, 2097088, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(12861, 2097152, F128, 21) (dual of [2097152, 2097091, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 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
- discarding factors / shortening the dual code based on linear OA(12864, 2097155, F128, 22) (dual of [2097155, 2097091, 23]-code), using
- OOA 2-folding [i] based on linear OA(12864, 2097154, F128, 22) (dual of [2097154, 2097090, 23]-code), using
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(12876, 524363, F128, 4, 22) (dual of [(524363, 4), 2097376, 23]-NRT-code) | [i] | OOA Folding | |