Information on Result #1308311
Linear OA(4174, 4205, F4, 37) (dual of [4205, 4031, 38]-code), using 92 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 0, 0, 1, 4 times 0, 1, 8 times 0, 1, 13 times 0, 1, 22 times 0, 1, 34 times 0) based on linear OA(4164, 4103, F4, 37) (dual of [4103, 3939, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(34) [i] based on
- linear OA(4163, 4096, F4, 37) (dual of [4096, 3933, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(4157, 4096, F4, 35) (dual of [4096, 3939, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [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: 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(4174, 4205, F4, 2, 37) (dual of [(4205, 2), 8236, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4174, 4205, F4, 3, 37) (dual of [(4205, 3), 12441, 38]-NRT-code) | [i] | ||
| 3 | Digital (137, 174, 4205)-net over F4 | [i] | ||
| 4 | Linear OOA(4174, 2102, F4, 2, 37) (dual of [(2102, 2), 4030, 38]-NRT-code) | [i] | OOA Folding | |