Information on Result #682188
Linear OA(587, 1953157, F5, 12) (dual of [1953157, 1953070, 13]-code), using construction X applied to Ce(11) ⊂ Ce(7) based on
- linear OA(582, 1953125, F5, 12) (dual of [1953125, 1953043, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(555, 1953125, F5, 8) (dual of [1953125, 1953070, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(55, 32, F5, 3) (dual of [32, 27, 4]-code or 32-cap in PG(4,5)), using
- discarding factors / shortening the dual code based on linear OA(55, 42, F5, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,5)), 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(588, 1953158, F5, 12) (dual of [1953158, 1953070, 13]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(587, 1161598, F5, 2, 12) (dual of [(1161598, 2), 2323109, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(587, 1161598, F5, 3, 12) (dual of [(1161598, 3), 3484707, 13]-NRT-code) | [i] | ||
| 4 | Digital (75, 87, 1161598)-net over F5 | [i] | ||
| 5 | Linear OOA(587, 976578, F5, 2, 12) (dual of [(976578, 2), 1953069, 13]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(587, 651052, F5, 3, 12) (dual of [(651052, 3), 1953069, 13]-NRT-code) | [i] | ||
| 7 | Linear OOA(587, 325526, F5, 12, 12) (dual of [(325526, 12), 3906225, 13]-NRT-code) | [i] | OA Folding and Stacking | |