Information on Result #2241247
Linear OA(495, 1048610, F4, 12) (dual of [1048610, 1048515, 13]-code), using 1 times truncation based on linear OA(496, 1048611, F4, 13) (dual of [1048611, 1048515, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(8) [i] based on
- linear OA(491, 1048576, F4, 13) (dual of [1048576, 1048485, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(461, 1048576, F4, 9) (dual of [1048576, 1048515, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(45, 35, F4, 3) (dual of [35, 30, 4]-code or 35-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), 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(497, 1048612, F4, 12) (dual of [1048612, 1048515, 13]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(495, 688992, F4, 2, 12) (dual of [(688992, 2), 1377889, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(495, 688992, F4, 3, 12) (dual of [(688992, 3), 2066881, 13]-NRT-code) | [i] | ||
| 4 | Digital (83, 95, 688992)-net over F4 | [i] | ||
| 5 | Linear OA(497, 1048613, F4, 12) (dual of [1048613, 1048516, 13]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(495, 524305, F4, 2, 12) (dual of [(524305, 2), 1048515, 13]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(495, 349536, F4, 3, 12) (dual of [(349536, 3), 1048513, 13]-NRT-code) | [i] | ||
| 8 | Linear OOA(495, 174768, F4, 12, 12) (dual of [(174768, 12), 2097121, 13]-NRT-code) | [i] | OA Folding and Stacking | |