Information on Result #677981
Linear OA(494, 4194342, F4, 11) (dual of [4194342, 4194248, 12]-code), using construction X applied to Ce(10) ⊂ Ce(6) based on
- linear OA(489, 4194304, F4, 11) (dual of [4194304, 4194215, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(456, 4194304, F4, 7) (dual of [4194304, 4194248, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(45, 38, F4, 3) (dual of [38, 33, 4]-code or 38-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(495, 4194343, F4, 11) (dual of [4194343, 4194248, 12]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(494, 2300994, F4, 2, 11) (dual of [(2300994, 2), 4601894, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(494, 2300994, F4, 3, 11) (dual of [(2300994, 3), 6902888, 12]-NRT-code) | [i] | ||
| 4 | Digital (83, 94, 2300994)-net over F4 | [i] | ||
| 5 | Linear OOA(494, 2097171, F4, 2, 11) (dual of [(2097171, 2), 4194248, 12]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(494, 1398114, F4, 3, 11) (dual of [(1398114, 3), 4194248, 12]-NRT-code) | [i] | ||
| 7 | Linear OOA(494, 838868, F4, 11, 11) (dual of [(838868, 11), 9227454, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |