Information on Result #679734
Linear OA(458, 4117, F4, 12) (dual of [4117, 4059, 13]-code), using construction X applied to Ce(12) ⊂ Ce(8) based on
- 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(437, 4096, F4, 9) (dual of [4096, 4059, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
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 OOA(458, 4072, F4, 2, 12) (dual of [(4072, 2), 8086, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(458, 4072, F4, 3, 12) (dual of [(4072, 3), 12158, 13]-NRT-code) | [i] | ||
| 3 | Digital (46, 58, 4072)-net over F4 | [i] | ||
| 4 | Linear OA(459, 4119, F4, 12) (dual of [4119, 4060, 13]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OA(460, 4121, F4, 12) (dual of [4121, 4061, 13]-code) | [i] | ||
| 6 | Linear OA(461, 4123, F4, 12) (dual of [4123, 4062, 13]-code) | [i] | ||
| 7 | Linear OOA(458, 2058, F4, 2, 12) (dual of [(2058, 2), 4058, 13]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(458, 1372, F4, 3, 12) (dual of [(1372, 3), 4058, 13]-NRT-code) | [i] | ||