Information on Result #679654
Linear OA(468, 4109, F4, 15) (dual of [4109, 4041, 16]-code), using construction X applied to Ce(14) ⊂ Ce(12) based on
- linear OA(467, 4096, F4, 15) (dual of [4096, 4029, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(455, 4096, F4, 13) (dual of [4096, 4041, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(41, 13, F4, 1) (dual of [13, 12, 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(469, 4110, F4, 15) (dual of [4110, 4041, 16]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(468, 2385, F4, 2, 15) (dual of [(2385, 2), 4702, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(468, 2385, F4, 3, 15) (dual of [(2385, 3), 7087, 16]-NRT-code) | [i] | ||
| 4 | Digital (53, 68, 2385)-net over F4 | [i] | ||
| 5 | Linear OA(471, 4116, F4, 15) (dual of [4116, 4045, 16]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OA(472, 4123, F4, 15) (dual of [4123, 4051, 16]-code) | [i] | ||
| 7 | Linear OA(473, 4137, F4, 15) (dual of [4137, 4064, 16]-code) | [i] | ||
| 8 | Linear OA(474, 4164, F4, 15) (dual of [4164, 4090, 16]-code) | [i] | ||
| 9 | Linear OOA(468, 2054, F4, 2, 15) (dual of [(2054, 2), 4040, 16]-NRT-code) | [i] | OOA Folding | |
| 10 | Linear OOA(468, 1369, F4, 3, 15) (dual of [(1369, 3), 4039, 16]-NRT-code) | [i] | ||