Information on Result #1308626
Linear OA(4213, 4250, F4, 46) (dual of [4250, 4037, 47]-code), using 140 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 1, 4 times 0, 1, 10 times 0, 1, 20 times 0, 1, 37 times 0, 1, 61 times 0) based on linear OA(4205, 4102, F4, 46) (dual of [4102, 3897, 47]-code), using
- construction X applied to Ce(45) ⊂ Ce(44) [i] based on
- linear OA(4205, 4096, F4, 46) (dual of [4096, 3891, 47]-code), using an extension Ce(45) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(4199, 4096, F4, 45) (dual of [4096, 3897, 46]-code), using an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [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(4213, 4250, F4, 2, 46) (dual of [(4250, 2), 8287, 47]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4213, 4250, F4, 3, 46) (dual of [(4250, 3), 12537, 47]-NRT-code) | [i] | ||
| 3 | Digital (167, 213, 4250)-net over F4 | [i] | ||
| 4 | Linear OOA(4213, 2125, F4, 2, 46) (dual of [(2125, 2), 4037, 47]-NRT-code) | [i] | OOA Folding | |