Information on Result #682125
Linear OA(5114, 1953167, F5, 15) (dual of [1953167, 1953053, 16]-code), using construction X applied to C([0,7]) ⊂ C([0,5]) based on
- linear OA(5109, 1953126, F5, 15) (dual of [1953126, 1953017, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 1953126 | 518−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(573, 1953126, F5, 11) (dual of [1953126, 1953053, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 1953126 | 518−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(55, 41, F5, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,5)), using
- discarding factors / shortening the dual code based on linear OA(55, 42, F5, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,5)), 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(5115, 1953168, F5, 15) (dual of [1953168, 1953053, 16]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(5116, 1953169, F5, 15) (dual of [1953169, 1953053, 16]-code) | [i] | ||
| 3 | Linear OA(5117, 1953170, F5, 15) (dual of [1953170, 1953053, 16]-code) | [i] | ||
| 4 | Linear OA(5118, 1953171, F5, 15) (dual of [1953171, 1953053, 16]-code) | [i] | ||
| 5 | Linear OOA(5114, 1686577, F5, 2, 15) (dual of [(1686577, 2), 3373040, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(5114, 1686577, F5, 3, 15) (dual of [(1686577, 3), 5059617, 16]-NRT-code) | [i] | ||
| 7 | Digital (99, 114, 1686577)-net over F5 | [i] | ||
| 8 | Linear OA(5116, 1953170, F5, 15) (dual of [1953170, 1953054, 16]-code) | [i] | Construction X with Varšamov Bound | |
| 9 | Linear OA(5117, 1953172, F5, 15) (dual of [1953172, 1953055, 16]-code) | [i] | ||
| 10 | Linear OA(5118, 1953174, F5, 15) (dual of [1953174, 1953056, 16]-code) | [i] | ||
| 11 | Linear OOA(5114, 976583, F5, 2, 15) (dual of [(976583, 2), 1953052, 16]-NRT-code) | [i] | OOA Folding | |
| 12 | Linear OOA(5114, 651055, F5, 3, 15) (dual of [(651055, 3), 1953051, 16]-NRT-code) | [i] | ||
| 13 | Linear OOA(5114, 279023, F5, 15, 15) (dual of [(279023, 15), 4185231, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |