Information on Result #698734
Linear OA(6433, 4098, F64, 17) (dual of [4098, 4065, 18]-code), using construction X applied to Ce(16) ⊂ Ce(15) based on
- 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(6431, 4096, F64, 16) (dual of [4096, 4065, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(866, 8196, F8, 17) (dual of [8196, 8130, 18]-code) | [i] | Trace Code | |
| 2 | OA(3240, 4098, S32, 17) | [i] | Discarding Parts of the Base for OAs | |
| 3 | Linear OA(6441, 4163, F64, 17) (dual of [4163, 4122, 18]-code) | [i] | (u, u+v)-Construction | |
| 4 | Linear OA(6442, 4178, F64, 17) (dual of [4178, 4136, 18]-code) | [i] | ||
| 5 | Linear OA(6443, 4180, F64, 17) (dual of [4180, 4137, 18]-code) | [i] | ||
| 6 | Linear OA(6444, 4202, F64, 17) (dual of [4202, 4158, 18]-code) | [i] | ||
| 7 | Linear OA(6445, 4228, F64, 17) (dual of [4228, 4183, 18]-code) | [i] | ||
| 8 | Linear OA(6446, 4295, F64, 17) (dual of [4295, 4249, 18]-code) | [i] | ||
| 9 | Linear OA(6447, 4553, F64, 17) (dual of [4553, 4506, 18]-code) | [i] | ||
| 10 | Linear OA(6438, 4127, F64, 17) (dual of [4127, 4089, 18]-code) | [i] | Varšamov–Edel Lengthening | |
| 11 | Linear OA(6439, 4198, F64, 17) (dual of [4198, 4159, 18]-code) | [i] | ||
| 12 | Linear OA(6440, 4408, F64, 17) (dual of [4408, 4368, 18]-code) | [i] | ||
| 13 | Linear OA(6441, 4941, F64, 17) (dual of [4941, 4900, 18]-code) | [i] | ||
| 14 | Linear OA(6442, 6031, F64, 17) (dual of [6031, 5989, 18]-code) | [i] | ||
| 15 | Linear OOA(6433, 2049, F64, 2, 17) (dual of [(2049, 2), 4065, 18]-NRT-code) | [i] | OOA Folding | |
| 16 | Linear OOA(6433, 1366, F64, 3, 17) (dual of [(1366, 3), 4065, 18]-NRT-code) | [i] | ||