Information on Result #679563
Linear OA(4247, 4102, F4, 55) (dual of [4102, 3855, 56]-code), using construction X applied to Ce(54) ⊂ Ce(53) based on
- linear OA(4247, 4096, F4, 55) (dual of [4096, 3849, 56]-code), using an extension Ce(54) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,54], and designed minimum distance d ≥ |I|+1 = 55 [i]
- 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(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 OOA(4247, 4102, F4, 2, 55) (dual of [(4102, 2), 7957, 56]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4247, 4102, F4, 3, 55) (dual of [(4102, 3), 12059, 56]-NRT-code) | [i] | ||
| 3 | Digital (192, 247, 4102)-net over F4 | [i] | ||
| 4 | Linear OA(4248, 4142, F4, 55) (dual of [4142, 3894, 56]-code) | [i] | Varšamov–Edel Lengthening | |
| 5 | Linear OA(4249, 4216, F4, 55) (dual of [4216, 3967, 56]-code) | [i] | ||
| 6 | Linear OA(4250, 4314, F4, 55) (dual of [4314, 4064, 56]-code) | [i] | ||
| 7 | Linear OA(4251, 4422, F4, 55) (dual of [4422, 4171, 56]-code) | [i] | ||
| 8 | Linear OA(4252, 4536, F4, 55) (dual of [4536, 4284, 56]-code) | [i] | ||
| 9 | Linear OOA(4247, 2051, F4, 2, 55) (dual of [(2051, 2), 3855, 56]-NRT-code) | [i] | OOA Folding | |
| 10 | Linear OOA(4247, 1367, F4, 3, 55) (dual of [(1367, 3), 3854, 56]-NRT-code) | [i] | ||