Information on Result #682378
Linear OA(5142, 78141, F5, 25) (dual of [78141, 77999, 26]-code), using construction X applied to C([0,12]) ⊂ C([0,11]) based on
- linear OA(5141, 78126, F5, 25) (dual of [78126, 77985, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(5127, 78126, F5, 23) (dual of [78126, 77999, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(51, 15, F5, 1) (dual of [15, 14, 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(5143, 78142, F5, 25) (dual of [78142, 77999, 26]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(5142, 45418, F5, 2, 25) (dual of [(45418, 2), 90694, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(5142, 45418, F5, 3, 25) (dual of [(45418, 3), 136112, 26]-NRT-code) | [i] | ||
| 4 | Digital (117, 142, 45418)-net over F5 | [i] | ||
| 5 | Linear OOA(5142, 39070, F5, 2, 25) (dual of [(39070, 2), 77998, 26]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(5142, 26047, F5, 3, 25) (dual of [(26047, 3), 77999, 26]-NRT-code) | [i] | ||
| 7 | Linear OOA(5142, 6511, F5, 25, 25) (dual of [(6511, 25), 162633, 26]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |