Information on Result #678730
Linear OA(4192, 65575, F4, 31) (dual of [65575, 65383, 32]-code), using construction X applied to Ce(30) ⊂ Ce(25) 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 OA(4193, 65576, F4, 31) (dual of [65576, 65383, 32]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4194, 65577, F4, 31) (dual of [65577, 65383, 32]-code) | [i] | ||
| 3 | Linear OOA(4192, 35893, F4, 2, 31) (dual of [(35893, 2), 71594, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(4192, 35893, F4, 3, 31) (dual of [(35893, 3), 107487, 32]-NRT-code) | [i] | ||
| 5 | Digital (161, 192, 35893)-net over F4 | [i] | ||
| 6 | Linear OOA(4192, 32787, F4, 2, 31) (dual of [(32787, 2), 65382, 32]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(4192, 21858, F4, 3, 31) (dual of [(21858, 3), 65382, 32]-NRT-code) | [i] | ||