Information on Result #1312160
Linear OA(869, 4834, F8, 18) (dual of [4834, 4765, 19]-code), using 726 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 0, 1, 10 times 0, 1, 32 times 0, 1, 86 times 0, 1, 204 times 0, 1, 384 times 0) based on linear OA(861, 4100, F8, 18) (dual of [4100, 4039, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(861, 4096, F8, 18) (dual of [4096, 4035, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- 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(80, 4, F8, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: 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 OOA(869, 4834, F8, 2, 18) (dual of [(4834, 2), 9599, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(869, 4834, F8, 3, 18) (dual of [(4834, 3), 14433, 19]-NRT-code) | [i] | ||
| 3 | Digital (51, 69, 4834)-net over F8 | [i] | ||
| 4 | Linear OOA(869, 2417, F8, 2, 18) (dual of [(2417, 2), 4765, 19]-NRT-code) | [i] | OOA Folding | |