Information on Result #2272831
Linear OA(4193, 65576, F4, 31) (dual of [65576, 65383, 32]-code), using 1 times code embedding in larger space based on linear OA(4192, 65575, F4, 31) (dual of [65575, 65383, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(25) [i] based on
- linear OA(4185, 65536, F4, 31) (dual of [65536, 65351, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(4153, 65536, F4, 26) (dual of [65536, 65383, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(47, 39, F4, 4) (dual of [39, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), 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(4193, 37652, F4, 2, 31) (dual of [(37652, 2), 75111, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4193, 37652, F4, 3, 31) (dual of [(37652, 3), 112763, 32]-NRT-code) | [i] | ||
| 3 | Digital (162, 193, 37652)-net over F4 | [i] | ||
| 4 | Linear OOA(4193, 32788, F4, 2, 31) (dual of [(32788, 2), 65383, 32]-NRT-code) | [i] | OOA Folding | |