Information on Result #682340
Linear OA(5133, 390685, F5, 19) (dual of [390685, 390552, 20]-code), using construction X applied to Ce(18) ⊂ Ce(11) based on
- linear OA(5121, 390625, F5, 19) (dual of [390625, 390504, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(573, 390625, F5, 12) (dual of [390625, 390552, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(512, 60, F5, 6) (dual of [60, 48, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(512, 62, F5, 6) (dual of [62, 50, 7]-code), using
- the cyclic code C(A) with length 62 | 53−1, defining set A = {4,8,11,17}, and minimum distance d ≥ |{8,11,14,…,23}|+1 = 7 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(512, 62, F5, 6) (dual of [62, 50, 7]-code), 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(5134, 390686, F5, 19) (dual of [390686, 390552, 20]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(5135, 390687, F5, 19) (dual of [390687, 390552, 20]-code) | [i] | ||
| 3 | Linear OOA(5133, 390685, F5, 2, 19) (dual of [(390685, 2), 781237, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(5133, 390685, F5, 3, 19) (dual of [(390685, 3), 1171922, 20]-NRT-code) | [i] | ||
| 5 | Digital (114, 133, 390685)-net over F5 | [i] | ||
| 6 | Linear OA(5134, 390687, F5, 19) (dual of [390687, 390553, 20]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OA(5135, 390689, F5, 19) (dual of [390689, 390554, 20]-code) | [i] | ||
| 8 | Linear OOA(5133, 195342, F5, 2, 19) (dual of [(195342, 2), 390551, 20]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(5133, 130228, F5, 3, 19) (dual of [(130228, 3), 390551, 20]-NRT-code) | [i] | ||
| 10 | Linear OOA(5133, 43409, F5, 19, 19) (dual of [(43409, 19), 824638, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |