Information on Result #692959
Linear OA(16100, 287, F16, 51) (dual of [287, 187, 52]-code), using construction X applied to Ce(50) ⊂ Ce(38) based on
- linear OA(1687, 256, F16, 51) (dual of [256, 169, 52]-code), using an extension Ce(50) of the primitive narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [1,50], and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(1669, 256, F16, 39) (dual of [256, 187, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(1613, 31, F16, 11) (dual of [31, 18, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(1613, 33, F16, 11) (dual of [33, 20, 12]-code), using
- extended algebraic-geometric code AGe(F,21P) [i] based on function field F/F16 with g(F) = 2 and N(F) ≥ 33, using
- discarding factors / shortening the dual code based on linear OA(1613, 33, F16, 11) (dual of [33, 20, 12]-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 OA(1699, 286, F16, 50) (dual of [286, 187, 51]-code) | [i] | Truncation | |
| 2 | Linear OOA(16100, 143, F16, 2, 51) (dual of [(143, 2), 186, 52]-NRT-code) | [i] | OOA Folding | |