Information on Result #692425
Linear OA(16129, 4158, F16, 39) (dual of [4158, 4029, 40]-code), using construction X applied to Ce(38) ⊂ Ce(23) based on
- linear OA(16109, 4096, F16, 39) (dual of [4096, 3987, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(1667, 4096, F16, 24) (dual of [4096, 4029, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(1620, 62, F16, 14) (dual of [62, 42, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(1620, 64, F16, 14) (dual of [64, 44, 15]-code), using
- algebraic-geometric code AG(F,49P) [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,49P) [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(1620, 64, F16, 14) (dual of [64, 44, 15]-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(16129, 2079, F16, 2, 39) (dual of [(2079, 2), 4029, 40]-NRT-code) | [i] | OOA Folding | |