Information on Result #678681
Linear OA(450, 65554, F4, 8) (dual of [65554, 65504, 9]-code), using construction X4 applied to Ce(8) ⊂ Ce(5) based on
- linear OA(449, 65536, F4, 9) (dual of [65536, 65487, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(433, 65536, F4, 6) (dual of [65536, 65503, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(417, 18, F4, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,4)), using
- dual of repetition code with length 18 [i]
- linear OA(41, 18, F4, 1) (dual of [18, 17, 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(451, 65555, F4, 8) (dual of [65555, 65504, 9]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(450, 65554, F4, 2, 8) (dual of [(65554, 2), 131058, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(450, 65554, F4, 3, 8) (dual of [(65554, 3), 196612, 9]-NRT-code) | [i] | ||
| 4 | Digital (42, 50, 65554)-net over F4 | [i] | ||
| 5 | Linear OA(451, 65556, F4, 8) (dual of [65556, 65505, 9]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OA(452, 65558, F4, 8) (dual of [65558, 65506, 9]-code) | [i] | ||
| 7 | Linear OOA(450, 32777, F4, 2, 8) (dual of [(32777, 2), 65504, 9]-NRT-code) | [i] | OOA Folding | |