Information on Result #679613
Linear OA(426, 4104, F4, 6) (dual of [4104, 4078, 7]-code), using construction X4 applied to Ce(5) ⊂ Ce(4) based on
- linear OA(425, 4096, F4, 6) (dual of [4096, 4071, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(419, 4096, F4, 5) (dual of [4096, 4077, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(47, 8, F4, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,4)), using
- dual of repetition code with length 8 [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
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(427, 4105, F4, 6) (dual of [4105, 4078, 7]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(426, 4104, F4, 2, 6) (dual of [(4104, 2), 8182, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(426, 4104, F4, 3, 6) (dual of [(4104, 3), 12286, 7]-NRT-code) | [i] | ||
| 4 | Digital (20, 26, 4104)-net over F4 | [i] | ||
| 5 | Linear OA(427, 4109, F4, 6) (dual of [4109, 4082, 7]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OOA(426, 2052, F4, 2, 6) (dual of [(2052, 2), 4078, 7]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(426, 1368, F4, 3, 6) (dual of [(1368, 3), 4078, 7]-NRT-code) | [i] | ||
| 8 | Linear OOA(426, 1368, F4, 6, 6) (dual of [(1368, 6), 8182, 7]-NRT-code) | [i] | OA Folding and Stacking | |