Information on Result #679929
Linear OA(4189, 4105, F4, 42) (dual of [4105, 3916, 43]-code), using construction XX applied to Ce(41) ⊂ Ce(40) ⊂ Ce(38) based on
- linear OA(4187, 4096, F4, 42) (dual of [4096, 3909, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [i]
- 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(4175, 4096, F4, 39) (dual of [4096, 3921, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(40, 7, F4, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(41, 2, F4, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [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(4189, 3520, F4, 2, 42) (dual of [(3520, 2), 6851, 43]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4189, 3520, F4, 3, 42) (dual of [(3520, 3), 10371, 43]-NRT-code) | [i] | ||
| 3 | Digital (147, 189, 3520)-net over F4 | [i] | ||
| 4 | Linear OOA(4189, 1368, F4, 3, 42) (dual of [(1368, 3), 3915, 43]-NRT-code) | [i] | OOA Folding | |