Information on Result #682203
Linear OA(578, 1953166, F5, 10) (dual of [1953166, 1953088, 11]-code), using construction X applied to Ce(10) ⊂ Ce(5) based on
- linear OA(573, 1953125, F5, 11) (dual of [1953125, 1953052, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(537, 1953125, F5, 6) (dual of [1953125, 1953088, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(55, 41, F5, 3) (dual of [41, 36, 4]-code or 41-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 OOA(578, 1953166, F5, 2, 10) (dual of [(1953166, 2), 3906254, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(578, 1953166, F5, 3, 10) (dual of [(1953166, 3), 5859420, 11]-NRT-code) | [i] | ||
| 3 | Digital (68, 78, 1953166)-net over F5 | [i] | ||
| 4 | Linear OA(579, 1953168, F5, 10) (dual of [1953168, 1953089, 11]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(578, 976583, F5, 2, 10) (dual of [(976583, 2), 1953088, 11]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(578, 651055, F5, 3, 10) (dual of [(651055, 3), 1953087, 11]-NRT-code) | [i] | ||
| 7 | Linear OOA(578, 390633, F5, 10, 10) (dual of [(390633, 10), 3906252, 11]-NRT-code) | [i] | OA Folding and Stacking | |