Information on Result #692036
Linear OA(1692, 4100, F16, 33) (dual of [4100, 4008, 34]-code), using construction X applied to Ce(32) ⊂ Ce(30) 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(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(161, 4, F16, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(1691, 4099, F16, 32) (dual of [4099, 4008, 33]-code) | [i] | Truncation | |
| 2 | Linear OA(16114, 4165, F16, 33) (dual of [4165, 4051, 34]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(16115, 4167, F16, 33) (dual of [4167, 4052, 34]-code) | [i] | ||
| 4 | Linear OA(16116, 4169, F16, 33) (dual of [4169, 4053, 34]-code) | [i] | ||
| 5 | Linear OA(16117, 4171, F16, 33) (dual of [4171, 4054, 34]-code) | [i] | ||
| 6 | Linear OOA(1692, 2819, F16, 2, 33) (dual of [(2819, 2), 5546, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 7 | Digital (59, 92, 2819)-net over F16 | [i] | ||
| 8 | Linear OOA(1692, 2050, F16, 2, 33) (dual of [(2050, 2), 4008, 34]-NRT-code) | [i] | OOA Folding | |