Information on Result #691723
Linear OA(16106, 1048636, F16, 20) (dual of [1048636, 1048530, 21]-code), using construction X applied to Ce(19) ⊂ Ce(9) based on
- linear OA(1691, 1048576, F16, 20) (dual of [1048576, 1048485, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(1646, 1048576, F16, 10) (dual of [1048576, 1048530, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(1615, 60, F16, 9) (dual of [60, 45, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(1615, 64, F16, 9) (dual of [64, 49, 10]-code), using
- algebraic-geometric code AG(F,54P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- algebraic-geometric code AG(F,54P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- discarding factors / shortening the dual code based on linear OA(1615, 64, F16, 9) (dual of [64, 49, 10]-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(16106, 524318, F16, 2, 20) (dual of [(524318, 2), 1048530, 21]-NRT-code) | [i] | OOA Folding | |