Information on Result #678711
Linear OA(4118, 65565, F4, 19) (dual of [65565, 65447, 20]-code), using construction X applied to Ce(18) ⊂ Ce(14) based on
- linear OA(4113, 65536, F4, 19) (dual of [65536, 65423, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(489, 65536, F4, 15) (dual of [65536, 65447, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(45, 29, F4, 3) (dual of [29, 24, 4]-code or 29-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 OOA(4118, 33284, F4, 2, 19) (dual of [(33284, 2), 66450, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4118, 33284, F4, 3, 19) (dual of [(33284, 3), 99734, 20]-NRT-code) | [i] | ||
| 3 | Digital (99, 118, 33284)-net over F4 | [i] | ||
| 4 | Linear OOA(4118, 32782, F4, 2, 19) (dual of [(32782, 2), 65446, 20]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4118, 21855, F4, 3, 19) (dual of [(21855, 3), 65447, 20]-NRT-code) | [i] | ||