Information on Result #691711
Linear OA(16110, 1048630, F16, 21) (dual of [1048630, 1048520, 22]-code), using construction X applied to Ce(20) ⊂ Ce(11) based on
- linear OA(1696, 1048576, F16, 21) (dual of [1048576, 1048480, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(1656, 1048576, F16, 12) (dual of [1048576, 1048520, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(1614, 54, F16, 8) (dual of [54, 40, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(1614, 64, F16, 8) (dual of [64, 50, 9]-code), using
- algebraic-geometric code AG(F,55P) [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,55P) [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(1614, 64, F16, 8) (dual of [64, 50, 9]-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(16110, 524315, F16, 2, 21) (dual of [(524315, 2), 1048520, 22]-NRT-code) | [i] | OOA Folding | |