Information on Result #679708
Linear OA(4132, 4119, F4, 29) (dual of [4119, 3987, 30]-code), using construction X applied to Ce(28) ⊂ Ce(24) based on
- linear OA(4127, 4096, F4, 29) (dual of [4096, 3969, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(45, 23, F4, 3) (dual of [23, 18, 4]-code or 23-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), 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(4132, 4119, F4, 28) (dual of [4119, 3987, 29]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(4133, 4120, F4, 29) (dual of [4120, 3987, 30]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(4131, 4118, F4, 28) (dual of [4118, 3987, 29]-code) | [i] | Truncation | |
| 4 | Linear OOA(4132, 3016, F4, 2, 29) (dual of [(3016, 2), 5900, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(4132, 3016, F4, 3, 29) (dual of [(3016, 3), 8916, 30]-NRT-code) | [i] | ||
| 6 | Digital (103, 132, 3016)-net over F4 | [i] | ||
| 7 | Linear OOA(4132, 2059, F4, 2, 29) (dual of [(2059, 2), 3986, 30]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(4132, 1373, F4, 3, 29) (dual of [(1373, 3), 3987, 30]-NRT-code) | [i] | ||