Information on Result #679578
Linear OA(4182, 4103, F4, 41) (dual of [4103, 3921, 42]-code), using construction X applied to Ce(40) ⊂ Ce(38) 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(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(41, 7, F4, 1) (dual of [7, 6, 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
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(4181, 4102, F4, 40) (dual of [4102, 3921, 41]-code) | [i] | Truncation | |
| 2 | Linear OOA(4182, 3164, F4, 2, 41) (dual of [(3164, 2), 6146, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(4182, 3164, F4, 3, 41) (dual of [(3164, 3), 9310, 42]-NRT-code) | [i] | ||
| 4 | Digital (141, 182, 3164)-net over F4 | [i] | ||
| 5 | Linear OA(4188, 4127, F4, 41) (dual of [4127, 3939, 42]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OOA(4182, 2051, F4, 2, 41) (dual of [(2051, 2), 3920, 42]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(4182, 1367, F4, 3, 41) (dual of [(1367, 3), 3919, 42]-NRT-code) | [i] | ||