Information on Result #679581
Linear OA(4164, 4103, F4, 37) (dual of [4103, 3939, 38]-code), using construction X applied to Ce(36) ⊂ Ce(34) 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: 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(4163, 4102, F4, 36) (dual of [4102, 3939, 37]-code) | [i] | Truncation | |
| 2 | Linear OOA(4164, 2924, F4, 2, 37) (dual of [(2924, 2), 5684, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(4164, 2924, F4, 3, 37) (dual of [(2924, 3), 8608, 38]-NRT-code) | [i] | ||
| 4 | Digital (127, 164, 2924)-net over F4 | [i] | ||
| 5 | Linear OA(4171, 4130, F4, 37) (dual of [4130, 3959, 38]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OA(4172, 4145, F4, 37) (dual of [4145, 3973, 38]-code) | [i] | ||
| 7 | Linear OA(4173, 4169, F4, 37) (dual of [4169, 3996, 38]-code) | [i] | ||
| 8 | Linear OA(4174, 4205, F4, 37) (dual of [4205, 4031, 38]-code) | [i] | ||
| 9 | Linear OA(4175, 4259, F4, 37) (dual of [4259, 4084, 38]-code) | [i] | ||
| 10 | Linear OA(4176, 4336, F4, 37) (dual of [4336, 4160, 38]-code) | [i] | ||
| 11 | Linear OA(4177, 4439, F4, 37) (dual of [4439, 4262, 38]-code) | [i] | ||
| 12 | Linear OA(4178, 4570, F4, 37) (dual of [4570, 4392, 38]-code) | [i] | ||
| 13 | Linear OA(4179, 4726, F4, 37) (dual of [4726, 4547, 38]-code) | [i] | ||
| 14 | Linear OA(4180, 4900, F4, 37) (dual of [4900, 4720, 38]-code) | [i] | ||
| 15 | Linear OOA(4164, 2051, F4, 2, 37) (dual of [(2051, 2), 3938, 38]-NRT-code) | [i] | OOA Folding | |
| 16 | Linear OOA(4164, 1367, F4, 3, 37) (dual of [(1367, 3), 3937, 38]-NRT-code) | [i] | ||