Information on Result #678206
Linear OA(486, 1048611, F4, 11) (dual of [1048611, 1048525, 12]-code), using construction X applied to Ce(10) ⊂ Ce(6) based on
- linear OA(481, 1048576, F4, 11) (dual of [1048576, 1048495, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(451, 1048576, F4, 7) (dual of [1048576, 1048525, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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(487, 1048612, F4, 11) (dual of [1048612, 1048525, 12]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(486, 671040, F4, 2, 11) (dual of [(671040, 2), 1341994, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(486, 671040, F4, 3, 11) (dual of [(671040, 3), 2013034, 12]-NRT-code) | [i] | ||
| 4 | Digital (75, 86, 671040)-net over F4 | [i] | ||
| 5 | Linear OOA(486, 524305, F4, 2, 11) (dual of [(524305, 2), 1048524, 12]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(486, 349537, F4, 3, 11) (dual of [(349537, 3), 1048525, 12]-NRT-code) | [i] | ||
| 7 | Linear OOA(486, 209722, F4, 11, 11) (dual of [(209722, 11), 2306856, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |