Information on Result #679977
Linear OA(4117, 4105, F4, 26) (dual of [4105, 3988, 27]-code), using construction XX applied to Ce(25) ⊂ Ce(24) ⊂ Ce(22) based on
- linear OA(4115, 4096, F4, 26) (dual of [4096, 3981, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(4109, 4096, F4, 25) (dual of [4096, 3987, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(4103, 4096, F4, 23) (dual of [4096, 3993, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(40, 7, F4, 0) (dual of [7, 7, 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
- linear OA(41, 2, F4, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [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(4117, 2637, F4, 2, 26) (dual of [(2637, 2), 5157, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4117, 2637, F4, 3, 26) (dual of [(2637, 3), 7794, 27]-NRT-code) | [i] | ||
| 3 | Digital (91, 117, 2637)-net over F4 | [i] | ||
| 4 | Linear OOA(4117, 1368, F4, 3, 26) (dual of [(1368, 3), 3987, 27]-NRT-code) | [i] | OOA Folding | |