Information on Result #1308349
Linear OA(4178, 4192, F4, 38) (dual of [4192, 4014, 39]-code), using 81 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 4 times 0, 1, 7 times 0, 1, 12 times 0, 1, 19 times 0, 1, 31 times 0) based on linear OA(4169, 4102, F4, 38) (dual of [4102, 3933, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(36) [i] based on
- linear OA(4169, 4096, F4, 38) (dual of [4096, 3927, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- 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(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(4178, 4192, F4, 2, 38) (dual of [(4192, 2), 8206, 39]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4178, 4192, F4, 3, 38) (dual of [(4192, 3), 12398, 39]-NRT-code) | [i] | ||
| 3 | Digital (140, 178, 4192)-net over F4 | [i] | ||
| 4 | Linear OOA(4178, 2096, F4, 2, 38) (dual of [(2096, 2), 4014, 39]-NRT-code) | [i] | OOA Folding | |