Information on Result #679576
Linear OA(4187, 4102, F4, 42) (dual of [4102, 3915, 43]-code), using construction X applied to Ce(41) ⊂ Ce(40) 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: 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(4188, 4103, F4, 42) (dual of [4103, 3915, 43]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4193, 4130, F4, 42) (dual of [4130, 3937, 43]-code) | [i] | Varšamov–Edel Lengthening | |
| 3 | Linear OA(4194, 4151, F4, 42) (dual of [4151, 3957, 43]-code) | [i] | ||
| 4 | Linear OA(4195, 4186, F4, 42) (dual of [4186, 3991, 43]-code) | [i] | ||
| 5 | Linear OA(4196, 4240, F4, 42) (dual of [4240, 4044, 43]-code) | [i] | ||
| 6 | Linear OA(4197, 4316, F4, 42) (dual of [4316, 4119, 43]-code) | [i] | ||
| 7 | Linear OA(4198, 4417, F4, 42) (dual of [4417, 4219, 43]-code) | [i] | ||
| 8 | Linear OA(4199, 4541, F4, 42) (dual of [4541, 4342, 43]-code) | [i] | ||
| 9 | Linear OA(4200, 4682, F4, 42) (dual of [4682, 4482, 43]-code) | [i] | ||
| 10 | Linear OA(4201, 4836, F4, 42) (dual of [4836, 4635, 43]-code) | [i] | ||
| 11 | Linear OA(4202, 4999, F4, 42) (dual of [4999, 4797, 43]-code) | [i] | ||
| 12 | Linear OOA(4187, 2051, F4, 2, 42) (dual of [(2051, 2), 3915, 43]-NRT-code) | [i] | OOA Folding | |
| 13 | Linear OOA(4187, 1367, F4, 3, 42) (dual of [(1367, 3), 3914, 43]-NRT-code) | [i] | ||