Information on Result #691717
Linear OA(1695, 1048630, F16, 18) (dual of [1048630, 1048535, 19]-code), using construction X applied to Ce(17) ⊂ Ce(8) based on
- linear OA(1681, 1048576, F16, 18) (dual of [1048576, 1048495, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(1641, 1048576, F16, 9) (dual of [1048576, 1048535, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(1695, 524315, F16, 2, 18) (dual of [(524315, 2), 1048535, 19]-NRT-code) | [i] | OOA Folding | |