Information on Result #904986
Linear OOA(12852, 1048730, F128, 2, 15) (dual of [(1048730, 2), 2097408, 16]-NRT-code), using (u, u+v)-construction based on
- linear OOA(1288, 150, F128, 2, 7) (dual of [(150, 2), 292, 8]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,292P) [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- linear OOA(12844, 1048580, F128, 2, 15) (dual of [(1048580, 2), 2097116, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12844, 2097160, F128, 15) (dual of [2097160, 2097116, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(12843, 2097153, F128, 15) (dual of [2097153, 2097110, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(12837, 2097153, F128, 13) (dual of [2097153, 2097116, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [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 C([0,7]) ⊂ C([0,6]) [i] based on
- OOA 2-folding [i] based on linear OA(12844, 2097160, F128, 15) (dual of [2097160, 2097116, 16]-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(12852, 524365, F128, 4, 15) (dual of [(524365, 4), 2097408, 16]-NRT-code) | [i] | OOA Folding | |