Information on Result #679562
Linear OA(4254, 4103, F4, 57) (dual of [4103, 3849, 58]-code), using construction X applied to Ce(56) ⊂ Ce(54) based on
- linear OA(4253, 4096, F4, 57) (dual of [4096, 3843, 58]-code), using an extension Ce(56) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,56], and designed minimum distance d ≥ |I|+1 = 57 [i]
- 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(41, 7, F4, 1) (dual of [7, 6, 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
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(4253, 4102, F4, 56) (dual of [4102, 3849, 57]-code) | [i] | Truncation | |
| 2 | Linear OOA(4254, 4103, F4, 2, 57) (dual of [(4103, 2), 7952, 58]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(4254, 4103, F4, 3, 57) (dual of [(4103, 3), 12055, 58]-NRT-code) | [i] | ||
| 4 | Digital (197, 254, 4103)-net over F4 | [i] | ||
| 5 | Linear OA(4255, 4119, F4, 57) (dual of [4119, 3864, 58]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OOA(4254, 2051, F4, 2, 57) (dual of [(2051, 2), 3848, 58]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(4254, 1367, F4, 3, 57) (dual of [(1367, 3), 3847, 58]-NRT-code) | [i] | ||