Information on Result #2273794
Linear OA(4213, 4110, F4, 47) (dual of [4110, 3897, 48]-code), using 1 times code embedding in larger space based on linear OA(4212, 4109, F4, 47) (dual of [4109, 3897, 48]-code), using
- construction X applied to Ce(46) ⊂ Ce(44) [i] based on
- linear OA(4211, 4096, F4, 47) (dual of [4096, 3885, 48]-code), using an extension Ce(46) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [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(41, 13, F4, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(4213, 3996, F4, 2, 47) (dual of [(3996, 2), 7779, 48]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4213, 3996, F4, 3, 47) (dual of [(3996, 3), 11775, 48]-NRT-code) | [i] | ||
| 3 | Digital (166, 213, 3996)-net over F4 | [i] | ||
| 4 | Linear OOA(4213, 2055, F4, 2, 47) (dual of [(2055, 2), 3897, 48]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4213, 1370, F4, 3, 47) (dual of [(1370, 3), 3897, 48]-NRT-code) | [i] | ||