Information on Result #679564
Linear OA(4241, 4102, F4, 54) (dual of [4102, 3861, 55]-code), using construction X applied to Ce(53) ⊂ Ce(52) based on
- linear OA(4241, 4096, F4, 54) (dual of [4096, 3855, 55]-code), using an extension Ce(53) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,53], and designed minimum distance d ≥ |I|+1 = 54 [i]
- 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(40, 6, F4, 0) (dual of [6, 6, 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
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(4242, 4103, F4, 54) (dual of [4103, 3861, 55]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4242, 4105, F4, 54) (dual of [4105, 3863, 55]-code) | [i] | Varšamov–Edel Lengthening | |
| 3 | Linear OA(4243, 4116, F4, 54) (dual of [4116, 3873, 55]-code) | [i] | ||
| 4 | Linear OA(4244, 4148, F4, 54) (dual of [4148, 3904, 55]-code) | [i] | ||
| 5 | Linear OA(4245, 4215, F4, 54) (dual of [4215, 3970, 55]-code) | [i] | ||
| 6 | Linear OA(4246, 4310, F4, 54) (dual of [4310, 4064, 55]-code) | [i] | ||
| 7 | Linear OA(4247, 4418, F4, 54) (dual of [4418, 4171, 55]-code) | [i] | ||
| 8 | Linear OA(4242, 4104, F4, 54) (dual of [4104, 3862, 55]-code) | [i] | Construction X with Varšamov Bound | |
| 9 | Linear OA(4243, 4106, F4, 54) (dual of [4106, 3863, 55]-code) | [i] | ||
| 10 | Linear OOA(4241, 2051, F4, 2, 54) (dual of [(2051, 2), 3861, 55]-NRT-code) | [i] | OOA Folding | |
| 11 | Linear OOA(4241, 1367, F4, 3, 54) (dual of [(1367, 3), 3860, 55]-NRT-code) | [i] | ||