Information on Result #698735
Linear OA(6431, 4098, F64, 16) (dual of [4098, 4067, 17]-code), using construction X applied to Ce(15) ⊂ Ce(14) based on
- 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(6429, 4096, F64, 15) (dual of [4096, 4067, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(862, 8196, F8, 16) (dual of [8196, 8134, 17]-code) | [i] | Trace Code | |
| 2 | OA(3238, 4098, S32, 16) | [i] | Discarding Parts of the Base for OAs | |
| 3 | Linear OA(6439, 4163, F64, 16) (dual of [4163, 4124, 17]-code) | [i] | (u, u+v)-Construction | |
| 4 | Linear OA(6440, 4178, F64, 16) (dual of [4178, 4138, 17]-code) | [i] | ||
| 5 | Linear OA(6441, 4180, F64, 16) (dual of [4180, 4139, 17]-code) | [i] | ||
| 6 | Linear OA(6442, 4202, F64, 16) (dual of [4202, 4160, 17]-code) | [i] | ||
| 7 | Linear OA(6443, 4228, F64, 16) (dual of [4228, 4185, 17]-code) | [i] | ||
| 8 | Linear OA(6444, 4295, F64, 16) (dual of [4295, 4251, 17]-code) | [i] | ||
| 9 | Linear OA(6436, 4129, F64, 16) (dual of [4129, 4093, 17]-code) | [i] | Varšamov–Edel Lengthening | |
| 10 | Linear OA(6437, 4212, F64, 16) (dual of [4212, 4175, 17]-code) | [i] | ||
| 11 | Linear OA(6438, 4498, F64, 16) (dual of [4498, 4460, 17]-code) | [i] | ||
| 12 | Linear OA(6439, 5266, F64, 16) (dual of [5266, 5227, 17]-code) | [i] | ||
| 13 | Linear OOA(6431, 2049, F64, 2, 16) (dual of [(2049, 2), 4067, 17]-NRT-code) | [i] | OOA Folding | |
| 14 | Linear OOA(6431, 1366, F64, 3, 16) (dual of [(1366, 3), 4067, 17]-NRT-code) | [i] | ||