Information on Result #679908
Linear OA(4219, 4105, F4, 49) (dual of [4105, 3886, 50]-code), using construction XX applied to Ce(48) ⊂ Ce(46) ⊂ Ce(45) based on
- linear OA(4217, 4096, F4, 49) (dual of [4096, 3879, 50]-code), using an extension Ce(48) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,48], and designed minimum distance d ≥ |I|+1 = 49 [i]
- 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(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(41, 8, F4, 1) (dual of [8, 7, 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
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
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(4219, 3761, F4, 2, 49) (dual of [(3761, 2), 7303, 50]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4219, 3761, F4, 3, 49) (dual of [(3761, 3), 11064, 50]-NRT-code) | [i] | ||
| 3 | Digital (170, 219, 3761)-net over F4 | [i] | ||
| 4 | Linear OOA(4219, 2052, F4, 2, 49) (dual of [(2052, 2), 3885, 50]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4219, 1368, F4, 3, 49) (dual of [(1368, 3), 3885, 50]-NRT-code) | [i] | ||