Information on Result #1324192
Linear OA(4241, 65627, F4, 36) (dual of [65627, 65386, 37]-code), using construction X with Varšamov bound based on
- linear OA(4238, 65621, F4, 36) (dual of [65621, 65383, 37]-code), using
- construction X applied to Ce(36) ⊂ Ce(25) [i] based on
- linear OA(4217, 65536, F4, 37) (dual of [65536, 65319, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [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(421, 85, F4, 9) (dual of [85, 64, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(421, 86, F4, 9) (dual of [86, 65, 10]-code), using
- construction X applied to Ce(36) ⊂ Ce(25) [i] based on
- linear OA(4238, 65624, F4, 35) (dual of [65624, 65386, 36]-code), using Gilbert–Varšamov bound and bm = 4238 > Vbs−1(k−1) = 3374 632630 120892 429140 415355 504904 484036 002079 013715 352942 668628 677610 213511 207913 523185 990142 214927 725689 685215 922251 022300 652921 011817 676918 [i]
- linear OA(40, 3, F4, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: 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(4241, 65627, F4, 2, 36) (dual of [(65627, 2), 131013, 37]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4241, 65627, F4, 3, 36) (dual of [(65627, 3), 196640, 37]-NRT-code) | [i] | ||
| 3 | Digital (205, 241, 65627)-net over F4 | [i] | ||
| 4 | Linear OOA(4241, 32813, F4, 2, 36) (dual of [(32813, 2), 65385, 37]-NRT-code) | [i] | OOA Folding | |