Information on Result #682700
Linear OA(570, 15646, F5, 14) (dual of [15646, 15576, 15]-code), using construction X applied to Ce(13) ⊂ Ce(10) based on
- linear OA(567, 15625, F5, 14) (dual of [15625, 15558, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(549, 15625, F5, 11) (dual of [15625, 15576, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(53, 21, F5, 2) (dual of [21, 18, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), 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(571, 15647, F5, 14) (dual of [15647, 15576, 15]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(570, 13808, F5, 2, 14) (dual of [(13808, 2), 27546, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(570, 13808, F5, 3, 14) (dual of [(13808, 3), 41354, 15]-NRT-code) | [i] | ||
| 4 | Digital (56, 70, 13808)-net over F5 | [i] | ||
| 5 | Linear OA(571, 15648, F5, 14) (dual of [15648, 15577, 15]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OA(572, 15650, F5, 14) (dual of [15650, 15578, 15]-code) | [i] | ||
| 7 | Linear OOA(570, 7823, F5, 2, 14) (dual of [(7823, 2), 15576, 15]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(570, 5215, F5, 3, 14) (dual of [(5215, 3), 15575, 15]-NRT-code) | [i] | ||
| 9 | Linear OOA(570, 2235, F5, 14, 14) (dual of [(2235, 14), 31220, 15]-NRT-code) | [i] | OA Folding and Stacking | |