Information on Result #1323781
Linear OA(5138, 390674, F5, 20) (dual of [390674, 390536, 21]-code), using construction X applied to Ce(20) ⊂ Ce(13) based on
- linear OA(5129, 390625, F5, 21) (dual of [390625, 390496, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(589, 390625, F5, 14) (dual of [390625, 390536, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(59, 49, F5, 5) (dual of [49, 40, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(59, 62, F5, 5) (dual of [62, 53, 6]-code), using
- a “GraCyc†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(59, 62, F5, 5) (dual of [62, 53, 6]-code), using
Mode: 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(5138, 390674, F5, 2, 20) (dual of [(390674, 2), 781210, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5138, 390674, F5, 3, 20) (dual of [(390674, 3), 1171884, 21]-NRT-code) | [i] | ||
| 3 | Digital (118, 138, 390674)-net over F5 | [i] | ||
| 4 | Linear OA(5139, 390676, F5, 20) (dual of [390676, 390537, 21]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OA(5140, 390678, F5, 20) (dual of [390678, 390538, 21]-code) | [i] | ||
| 6 | Linear OOA(5138, 195337, F5, 2, 20) (dual of [(195337, 2), 390536, 21]-NRT-code) | [i] | OOA Folding | |