Information on Result #682662
Linear OA(5134, 15638, F5, 28) (dual of [15638, 15504, 29]-code), using construction X applied to Ce(27) ⊂ Ce(25) based on
- linear OA(5133, 15625, F5, 28) (dual of [15625, 15492, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(5121, 15625, F5, 26) (dual of [15625, 15504, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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 OA(5135, 15639, F5, 28) (dual of [15639, 15504, 29]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(5134, 9907, F5, 2, 28) (dual of [(9907, 2), 19680, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(5134, 9907, F5, 3, 28) (dual of [(9907, 3), 29587, 29]-NRT-code) | [i] | ||
| 4 | Digital (106, 134, 9907)-net over F5 | [i] | ||
| 5 | Linear OOA(5134, 7819, F5, 2, 28) (dual of [(7819, 2), 15504, 29]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(5134, 5212, F5, 3, 28) (dual of [(5212, 3), 15502, 29]-NRT-code) | [i] | ||
| 7 | Linear OOA(5134, 1117, F5, 28, 28) (dual of [(1117, 28), 31142, 29]-NRT-code) | [i] | OA Folding and Stacking | |