Information on Result #679933
Linear OA(4183, 4111, F4, 40) (dual of [4111, 3928, 41]-code), using construction XX applied to Ce(40) ⊂ Ce(37) ⊂ Ce(36) based on
- linear OA(4181, 4096, F4, 41) (dual of [4096, 3915, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(4169, 4096, F4, 38) (dual of [4096, 3927, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(4163, 4096, F4, 37) (dual of [4096, 3933, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(41, 14, F4, 1) (dual of [14, 13, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
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 OOA(4183, 3800, F4, 2, 40) (dual of [(3800, 2), 7417, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4183, 3800, F4, 3, 40) (dual of [(3800, 3), 11217, 41]-NRT-code) | [i] | ||
| 3 | Digital (143, 183, 3800)-net over F4 | [i] | ||
| 4 | Linear OOA(4183, 2055, F4, 2, 40) (dual of [(2055, 2), 3927, 41]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4183, 1370, F4, 3, 40) (dual of [(1370, 3), 3927, 41]-NRT-code) | [i] | ||