Information on Result #1308481
Linear OA(4195, 4186, F4, 42) (dual of [4186, 3991, 43]-code), using 76 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 5 times 0, 1, 11 times 0, 1, 19 times 0, 1, 33 times 0) based on linear OA(4187, 4102, F4, 42) (dual of [4102, 3915, 43]-code), using
- construction X applied to Ce(41) ⊂ Ce(40) [i] based on
- linear OA(4187, 4096, F4, 42) (dual of [4096, 3909, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(4181, 4096, F4, 41) (dual of [4096, 3915, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [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(4195, 4186, F4, 2, 42) (dual of [(4186, 2), 8177, 43]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4195, 4186, F4, 3, 42) (dual of [(4186, 3), 12363, 43]-NRT-code) | [i] | ||
| 3 | Digital (153, 195, 4186)-net over F4 | [i] | ||
| 4 | Linear OOA(4195, 2093, F4, 2, 42) (dual of [(2093, 2), 3991, 43]-NRT-code) | [i] | OOA Folding | |