Information on Result #682465
Linear OA(558, 78141, F5, 10) (dual of [78141, 78083, 11]-code), using construction X4 applied to Ce(10) ⊂ Ce(7) based on
- linear OA(557, 78125, F5, 11) (dual of [78125, 78068, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(543, 78125, F5, 8) (dual of [78125, 78082, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(515, 16, F5, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,5)), using
- dual of repetition code with length 16 [i]
- linear OA(51, 16, F5, 1) (dual of [16, 15, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(559, 78142, F5, 10) (dual of [78142, 78083, 11]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(558, 78141, F5, 2, 10) (dual of [(78141, 2), 156224, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(558, 78141, F5, 3, 10) (dual of [(78141, 3), 234365, 11]-NRT-code) | [i] | ||
| 4 | Digital (48, 58, 78141)-net over F5 | [i] | ||
| 5 | Linear OA(559, 78143, F5, 10) (dual of [78143, 78084, 11]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(558, 26047, F5, 3, 10) (dual of [(26047, 3), 78083, 11]-NRT-code) | [i] | OOA Folding | |