Information on Result #682456
Linear OA(5107, 78140, F5, 19) (dual of [78140, 78033, 20]-code), using construction X applied to Ce(18) ⊂ Ce(16) based on
- linear OA(5106, 78125, F5, 19) (dual of [78125, 78019, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(592, 78125, F5, 17) (dual of [78125, 78033, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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 OOA(5107, 40930, F5, 2, 19) (dual of [(40930, 2), 81753, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5107, 40930, F5, 3, 19) (dual of [(40930, 3), 122683, 20]-NRT-code) | [i] | ||
| 3 | Digital (88, 107, 40930)-net over F5 | [i] | ||
| 4 | Linear OOA(5107, 39070, F5, 2, 19) (dual of [(39070, 2), 78033, 20]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5107, 26046, F5, 3, 19) (dual of [(26046, 3), 78031, 20]-NRT-code) | [i] | ||
| 6 | Linear OOA(5107, 8682, F5, 19, 19) (dual of [(8682, 19), 164851, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |