Information on Result #692432
Linear OA(16107, 4157, F16, 31) (dual of [4157, 4050, 32]-code), using construction X applied to Ce(30) ⊂ Ce(16) based on
- linear OA(1688, 4096, F16, 31) (dual of [4096, 4008, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(1646, 4096, F16, 17) (dual of [4096, 4050, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(1619, 61, F16, 13) (dual of [61, 42, 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(16108, 4158, F16, 31) (dual of [4158, 4050, 32]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(16107, 2078, F16, 2, 31) (dual of [(2078, 2), 4049, 32]-NRT-code) | [i] | OOA Folding | |