Information on Result #679647
Linear OA(4104, 4109, F4, 23) (dual of [4109, 4005, 24]-code), using construction X applied to Ce(22) ⊂ Ce(20) based on
- 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(491, 4096, F4, 21) (dual of [4096, 4005, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(41, 13, F4, 1) (dual of [13, 12, 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(4105, 4110, F4, 23) (dual of [4110, 4005, 24]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4104, 2580, F4, 2, 23) (dual of [(2580, 2), 5056, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(4104, 2580, F4, 3, 23) (dual of [(2580, 3), 7636, 24]-NRT-code) | [i] | ||
| 4 | Digital (81, 104, 2580)-net over F4 | [i] | ||
| 5 | Linear OOA(4104, 2054, F4, 2, 23) (dual of [(2054, 2), 4004, 24]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(4104, 1369, F4, 3, 23) (dual of [(1369, 3), 4003, 24]-NRT-code) | [i] | ||