Information on Result #905122
Linear OOA(12872, 1048771, F128, 2, 20) (dual of [(1048771, 2), 2097470, 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(12859, 1048579, F128, 2, 20) (dual of [(1048579, 2), 2097099, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12859, 2097158, F128, 20) (dual of [2097158, 2097099, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(12859, 2097159, F128, 20) (dual of [2097159, 2097100, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(17) [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(12852, 2097152, F128, 18) (dual of [2097152, 2097100, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(1281, 7, F128, 1) (dual of [7, 6, 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 Ce(19) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(12859, 2097159, F128, 20) (dual of [2097159, 2097100, 21]-code), using
- OOA 2-folding [i] based on linear OA(12859, 2097158, F128, 20) (dual of [2097158, 2097099, 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(12872, 524385, F128, 4, 20) (dual of [(524385, 4), 2097468, 21]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(12872, 209754, F128, 22, 20) (dual of [(209754, 22), 4614516, 21]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |