Information on Result #698732
Linear OA(6435, 4098, F64, 18) (dual of [4098, 4063, 19]-code), using construction X applied to Ce(17) ⊂ Ce(16) based on
- linear OA(6435, 4096, F64, 18) (dual of [4096, 4061, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(6433, 4096, F64, 17) (dual of [4096, 4063, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(640, 2, F64, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-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(870, 8196, F8, 18) (dual of [8196, 8126, 19]-code) | [i] | Trace Code | |
| 2 | OA(3242, 4098, S32, 18) | [i] | Discarding Parts of the Base for OAs | |
| 3 | Linear OA(6444, 4163, F64, 18) (dual of [4163, 4119, 19]-code) | [i] | (u, u+v)-Construction | |
| 4 | Linear OA(6445, 4178, F64, 18) (dual of [4178, 4133, 19]-code) | [i] | ||
| 5 | Linear OA(6446, 4180, F64, 18) (dual of [4180, 4134, 19]-code) | [i] | ||
| 6 | Linear OA(6447, 4202, F64, 18) (dual of [4202, 4155, 19]-code) | [i] | ||
| 7 | Linear OA(6448, 4228, F64, 18) (dual of [4228, 4180, 19]-code) | [i] | ||
| 8 | Linear OA(6449, 4243, F64, 18) (dual of [4243, 4194, 19]-code) | [i] | ||
| 9 | Linear OA(6450, 4297, F64, 18) (dual of [4297, 4247, 19]-code) | [i] | ||
| 10 | Linear OA(6440, 4124, F64, 18) (dual of [4124, 4084, 19]-code) | [i] | Varšamov–Edel Lengthening | |
| 11 | Linear OA(6441, 4176, F64, 18) (dual of [4176, 4135, 19]-code) | [i] | ||
| 12 | Linear OA(6442, 4321, F64, 18) (dual of [4321, 4279, 19]-code) | [i] | ||
| 13 | Linear OA(6443, 4696, F64, 18) (dual of [4696, 4653, 19]-code) | [i] | ||
| 14 | Linear OA(6444, 5521, F64, 18) (dual of [5521, 5477, 19]-code) | [i] | ||
| 15 | Linear OOA(6435, 2049, F64, 2, 18) (dual of [(2049, 2), 4063, 19]-NRT-code) | [i] | OOA Folding | |
| 16 | Linear OOA(6435, 1366, F64, 3, 18) (dual of [(1366, 3), 4063, 19]-NRT-code) | [i] | ||