Information on Result #1019453
Linear OOA(12866, 699203, F128, 3, 19) (dual of [(699203, 3), 2097543, 20]-NRT-code), using (u, u+v)-construction based on
- linear OOA(12810, 150, F128, 3, 9) (dual of [(150, 3), 440, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,440P) [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- linear OOA(12856, 699053, F128, 3, 19) (dual of [(699053, 3), 2097103, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12856, 2097159, F128, 19) (dual of [2097159, 2097103, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(12856, 2097160, F128, 19) (dual of [2097160, 2097104, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- linear OA(12855, 2097153, F128, 19) (dual of [2097153, 2097098, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(12849, 2097153, F128, 17) (dual of [2097153, 2097104, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (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([0,9]) ⊂ C([0,8]) [i] based on
- discarding factors / shortening the dual code based on linear OA(12856, 2097160, F128, 19) (dual of [2097160, 2097104, 20]-code), using
- OOA 3-folding [i] based on linear OA(12856, 2097159, F128, 19) (dual of [2097159, 2097103, 20]-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(12866, 233067, F128, 21, 19) (dual of [(233067, 21), 4894341, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |