Information on Result #692420
Linear OA(16110, 4154, F16, 33) (dual of [4154, 4044, 34]-code), using construction X applied to Ce(32) ⊂ Ce(18) based on
- linear OA(1691, 4096, F16, 33) (dual of [4096, 4005, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(1652, 4096, F16, 19) (dual of [4096, 4044, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(1619, 58, F16, 13) (dual of [58, 39, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(1619, 64, F16, 13) (dual of [64, 45, 14]-code), using
- algebraic-geometric code AG(F,50P) [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,50P) [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(1619, 64, F16, 13) (dual of [64, 45, 14]-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(16109, 4153, F16, 32) (dual of [4153, 4044, 33]-code) | [i] | Truncation | |
| 2 | Linear OOA(16110, 2077, F16, 2, 33) (dual of [(2077, 2), 4044, 34]-NRT-code) | [i] | OOA Folding | |