Information on Result #687191
Linear OA(858, 4101, F8, 17) (dual of [4101, 4043, 18]-code), using construction X applied to Ce(16) ⊂ Ce(14) based on
- linear OA(857, 4096, F8, 17) (dual of [4096, 4039, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(853, 4096, F8, 15) (dual of [4096, 4043, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(81, 5, F8, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 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(857, 4100, F8, 16) (dual of [4100, 4043, 17]-code) | [i] | Truncation | |
| 2 | Linear OOA(858, 2471, F8, 2, 17) (dual of [(2471, 2), 4884, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(858, 2471, F8, 3, 17) (dual of [(2471, 3), 7355, 18]-NRT-code) | [i] | ||
| 4 | Digital (41, 58, 2471)-net over F8 | [i] | ||
| 5 | Linear OA(861, 4114, F8, 17) (dual of [4114, 4053, 18]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OA(862, 4138, F8, 17) (dual of [4138, 4076, 18]-code) | [i] | ||
| 7 | Linear OA(863, 4201, F8, 17) (dual of [4201, 4138, 18]-code) | [i] | ||
| 8 | Linear OA(864, 4357, F8, 17) (dual of [4357, 4293, 18]-code) | [i] | ||
| 9 | Linear OA(865, 4682, F8, 17) (dual of [4682, 4617, 18]-code) | [i] | ||
| 10 | Linear OOA(858, 2050, F8, 2, 17) (dual of [(2050, 2), 4042, 18]-NRT-code) | [i] | OOA Folding | |
| 11 | Linear OOA(858, 1367, F8, 3, 17) (dual of [(1367, 3), 4043, 18]-NRT-code) | [i] | ||