Information on Result #905116
Linear OOA(12871, 1048769, F128, 2, 20) (dual of [(1048769, 2), 2097467, 21]-NRT-code), using (u, u+v)-construction based on
- linear OOA(12813, 192, F128, 2, 10) (dual of [(192, 2), 371, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,373P) [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- linear OOA(12858, 1048577, F128, 2, 20) (dual of [(1048577, 2), 2097096, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12858, 2097154, F128, 20) (dual of [2097154, 2097096, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(12858, 2097155, F128, 20) (dual of [2097155, 2097097, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(12858, 2097152, F128, 20) (dual of [2097152, 2097094, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(12855, 2097152, F128, 19) (dual of [2097152, 2097097, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(19) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(12858, 2097155, F128, 20) (dual of [2097155, 2097097, 21]-code), using
- OOA 2-folding [i] based on linear OA(12858, 2097154, F128, 20) (dual of [2097154, 2097096, 21]-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(12871, 524384, F128, 4, 20) (dual of [(524384, 4), 2097465, 21]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(12871, 209753, F128, 22, 20) (dual of [(209753, 22), 4614495, 21]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |