Information on Result #679896
Linear OA(4237, 4105, F4, 53) (dual of [4105, 3868, 54]-code), using construction XX applied to Ce(52) ⊂ Ce(50) ⊂ Ce(49) based on
- linear OA(4235, 4096, F4, 53) (dual of [4096, 3861, 54]-code), using an extension Ce(52) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,52], and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(4229, 4096, F4, 51) (dual of [4096, 3867, 52]-code), using an extension Ce(50) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,50], and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(4223, 4096, F4, 50) (dual of [4096, 3873, 51]-code), using an extension Ce(49) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,49], and designed minimum distance d ≥ |I|+1 = 50 [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(4237, 4003, F4, 2, 53) (dual of [(4003, 2), 7769, 54]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4237, 4003, F4, 3, 53) (dual of [(4003, 3), 11772, 54]-NRT-code) | [i] | ||
| 3 | Digital (184, 237, 4003)-net over F4 | [i] | ||
| 4 | Linear OOA(4237, 2052, F4, 2, 53) (dual of [(2052, 2), 3867, 54]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4237, 1368, F4, 3, 53) (dual of [(1368, 3), 3867, 54]-NRT-code) | [i] | ||