Information on Result #679920
Linear OA(4201, 4105, F4, 45) (dual of [4105, 3904, 46]-code), using construction XX applied to Ce(44) ⊂ Ce(42) ⊂ Ce(41) 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(4193, 4096, F4, 43) (dual of [4096, 3903, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- 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(41, 8, F4, 1) (dual of [8, 7, 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(4201, 3519, F4, 2, 45) (dual of [(3519, 2), 6837, 46]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4201, 3519, F4, 3, 45) (dual of [(3519, 3), 10356, 46]-NRT-code) | [i] | ||
| 3 | Digital (156, 201, 3519)-net over F4 | [i] | ||
| 4 | Linear OOA(4201, 2052, F4, 2, 45) (dual of [(2052, 2), 3903, 46]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4201, 1368, F4, 3, 45) (dual of [(1368, 3), 3903, 46]-NRT-code) | [i] | ||