Information on Result #1308823
Linear OA(4235, 4415, F4, 51) (dual of [4415, 4180, 52]-code), using 307 step Varšamov–Edel lengthening with (ri) = (1, 0, 1, 7 times 0, 1, 26 times 0, 1, 61 times 0, 1, 94 times 0, 1, 112 times 0) based on linear OA(4229, 4102, F4, 51) (dual of [4102, 3873, 52]-code), using
- construction X applied to Ce(50) ⊂ Ce(49) [i] based on
- linear OA(4229, 4096, F4, 51) (dual of [4096, 3867, 52]-code), using an extension Ce(50) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,50], and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(4223, 4096, F4, 50) (dual of [4096, 3873, 51]-code), using an extension Ce(49) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,49], and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(40, 6, F4, 0) (dual of [6, 6, 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(4235, 4415, F4, 2, 51) (dual of [(4415, 2), 8595, 52]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4235, 4415, F4, 3, 51) (dual of [(4415, 3), 13010, 52]-NRT-code) | [i] | ||
| 3 | Digital (184, 235, 4415)-net over F4 | [i] | ||
| 4 | Linear OOA(4235, 2207, F4, 2, 51) (dual of [(2207, 2), 4179, 52]-NRT-code) | [i] | OOA Folding | |