Information on Result #682995
Linear OA(5117, 3136, F5, 29) (dual of [3136, 3019, 30]-code), using construction X applied to Ce(28) ⊂ Ce(26) based on
- linear OA(5116, 3125, F5, 29) (dual of [3125, 3009, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(5106, 3125, F5, 27) (dual of [3125, 3019, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(51, 11, F5, 1) (dual of [11, 10, 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(5117, 2731, F5, 2, 29) (dual of [(2731, 2), 5345, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5117, 2731, F5, 3, 29) (dual of [(2731, 3), 8076, 30]-NRT-code) | [i] | ||
| 3 | Digital (88, 117, 2731)-net over F5 | [i] | ||
| 4 | Linear OOA(5117, 1568, F5, 2, 29) (dual of [(1568, 2), 3019, 30]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5117, 1045, F5, 3, 29) (dual of [(1045, 3), 3018, 30]-NRT-code) | [i] | ||