Information on Result #692362
Linear OA(16126, 4140, F16, 40) (dual of [4140, 4014, 41]-code), using construction X applied to Ce(39) ⊂ Ce(28) based on
- linear OA(16112, 4096, F16, 40) (dual of [4096, 3984, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(1682, 4096, F16, 29) (dual of [4096, 4014, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(1614, 44, F16, 10) (dual of [44, 30, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(1614, 45, F16, 10) (dual of [45, 31, 11]-code), using
- extended algebraic-geometric code AGe(F,34P) [i] based on function field F/F16 with g(F) = 4 and N(F) ≥ 45, using
- discarding factors / shortening the dual code based on linear OA(1614, 45, F16, 10) (dual of [45, 31, 11]-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(16127, 4141, F16, 40) (dual of [4141, 4014, 41]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(16126, 2070, F16, 2, 40) (dual of [(2070, 2), 4014, 41]-NRT-code) | [i] | OOA Folding | |