Information on Result #679684
Linear OA(4204, 4119, F4, 45) (dual of [4119, 3915, 46]-code), using construction X applied to Ce(44) ⊂ Ce(40) based on
- linear OA(4199, 4096, F4, 45) (dual of [4096, 3897, 46]-code), using an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [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(45, 23, F4, 3) (dual of [23, 18, 4]-code or 23-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), 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(4204, 4119, F4, 44) (dual of [4119, 3915, 45]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(4205, 4120, F4, 45) (dual of [4120, 3915, 46]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(4203, 4118, F4, 44) (dual of [4118, 3915, 45]-code) | [i] | Truncation | |
| 4 | Linear OOA(4204, 3880, F4, 2, 45) (dual of [(3880, 2), 7556, 46]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(4204, 3880, F4, 3, 45) (dual of [(3880, 3), 11436, 46]-NRT-code) | [i] | ||
| 6 | Digital (159, 204, 3880)-net over F4 | [i] | ||
| 7 | Linear OOA(4204, 2059, F4, 2, 45) (dual of [(2059, 2), 3914, 46]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(4204, 1373, F4, 3, 45) (dual of [(1373, 3), 3915, 46]-NRT-code) | [i] | ||