Information on Result #682661
Linear OA(5140, 15638, F5, 29) (dual of [15638, 15498, 30]-code), using construction X applied to Ce(28) ⊂ Ce(26) based on
- linear OA(5139, 15625, F5, 29) (dual of [15625, 15486, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(5127, 15625, F5, 27) (dual of [15625, 15498, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(51, 13, F5, 1) (dual of [13, 12, 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 OOA(5140, 10814, F5, 2, 29) (dual of [(10814, 2), 21488, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5140, 10814, F5, 3, 29) (dual of [(10814, 3), 32302, 30]-NRT-code) | [i] | ||
| 3 | Digital (111, 140, 10814)-net over F5 | [i] | ||
| 4 | Linear OOA(5140, 7819, F5, 2, 29) (dual of [(7819, 2), 15498, 30]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5140, 5212, F5, 3, 29) (dual of [(5212, 3), 15496, 30]-NRT-code) | [i] | ||