Information on Result #692199
Linear OA(1666, 4116, F16, 22) (dual of [4116, 4050, 23]-code), using construction X applied to Ce(21) ⊂ Ce(16) based on
- linear OA(1661, 4096, F16, 22) (dual of [4096, 4035, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(165, 20, F16, 4) (dual of [20, 15, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(165, 24, F16, 4) (dual of [24, 19, 5]-code), using
- extended algebraic-geometric code AGe(F,19P) [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 24, using
- discarding factors / shortening the dual code based on linear OA(165, 24, F16, 4) (dual of [24, 19, 5]-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(1667, 4117, F16, 22) (dual of [4117, 4050, 23]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(1667, 4118, F16, 22) (dual of [4118, 4051, 23]-code) | [i] | Construction X with Varšamov Bound | |
| 3 | Linear OOA(1666, 2058, F16, 2, 22) (dual of [(2058, 2), 4050, 23]-NRT-code) | [i] | OOA Folding | |