Information on Result #679570
Linear OA(4218, 4103, F4, 49) (dual of [4103, 3885, 50]-code), using construction X applied to Ce(48) ⊂ Ce(46) 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(41, 7, F4, 1) (dual of [7, 6, 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 OA(4217, 4102, F4, 48) (dual of [4102, 3885, 49]-code) | [i] | Truncation | |
| 2 | Linear OOA(4218, 3650, F4, 2, 49) (dual of [(3650, 2), 7082, 50]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(4218, 3650, F4, 3, 49) (dual of [(3650, 3), 10732, 50]-NRT-code) | [i] | ||
| 4 | Digital (169, 218, 3650)-net over F4 | [i] | ||
| 5 | Linear OA(4222, 4124, F4, 49) (dual of [4124, 3902, 50]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OA(4223, 4144, F4, 49) (dual of [4144, 3921, 50]-code) | [i] | ||
| 7 | Linear OA(4224, 4180, F4, 49) (dual of [4180, 3956, 50]-code) | [i] | ||
| 8 | Linear OA(4225, 4239, F4, 49) (dual of [4239, 4014, 50]-code) | [i] | ||
| 9 | Linear OA(4226, 4323, F4, 49) (dual of [4323, 4097, 50]-code) | [i] | ||
| 10 | Linear OA(4227, 4430, F4, 49) (dual of [4430, 4203, 50]-code) | [i] | ||
| 11 | Linear OOA(4218, 2051, F4, 2, 49) (dual of [(2051, 2), 3884, 50]-NRT-code) | [i] | OOA Folding | |
| 12 | Linear OOA(4218, 1367, F4, 3, 49) (dual of [(1367, 3), 3883, 50]-NRT-code) | [i] | ||