Information on Result #682630
Linear OA(5146, 15632, F5, 31) (dual of [15632, 15486, 32]-code), using construction X applied to Ce(30) ⊂ Ce(28) based on
- linear OA(5145, 15625, F5, 31) (dual of [15625, 15480, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- 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(51, 7, F5, 1) (dual of [7, 6, 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(5145, 15631, F5, 30) (dual of [15631, 15486, 31]-code) | [i] | Truncation | |
| 2 | Linear OOA(5146, 9098, F5, 2, 31) (dual of [(9098, 2), 18050, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(5146, 9098, F5, 3, 31) (dual of [(9098, 3), 27148, 32]-NRT-code) | [i] | ||
| 4 | Digital (115, 146, 9098)-net over F5 | [i] | ||
| 5 | Linear OOA(5146, 7816, F5, 2, 31) (dual of [(7816, 2), 15486, 32]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(5146, 5210, F5, 3, 31) (dual of [(5210, 3), 15484, 32]-NRT-code) | [i] | ||
| 7 | Linear OOA(5146, 1042, F5, 31, 31) (dual of [(1042, 31), 32156, 32]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |