Information on Result #1307981
Linear OA(4130, 4194, F4, 27) (dual of [4194, 4064, 28]-code), using 83 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 4 times 0, 1, 7 times 0, 1, 12 times 0, 1, 20 times 0, 1, 32 times 0) based on linear OA(4121, 4102, F4, 27) (dual of [4102, 3981, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- linear OA(4121, 4096, F4, 27) (dual of [4096, 3975, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(4115, 4096, F4, 26) (dual of [4096, 3981, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(4130, 4194, F4, 2, 27) (dual of [(4194, 2), 8258, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4130, 4194, F4, 3, 27) (dual of [(4194, 3), 12452, 28]-NRT-code) | [i] | ||
| 3 | Digital (103, 130, 4194)-net over F4 | [i] | ||
| 4 | Linear OOA(4130, 2097, F4, 2, 27) (dual of [(2097, 2), 4064, 28]-NRT-code) | [i] | OOA Folding | |