Information on Result #682268
Linear OA(542, 390635, F5, 7) (dual of [390635, 390593, 8]-code), using construction X4 applied to Ce(6) ⊂ Ce(5) based on
- linear OA(541, 390625, F5, 7) (dual of [390625, 390584, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(533, 390625, F5, 6) (dual of [390625, 390592, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(59, 10, F5, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,5)), using
- dual of repetition code with length 10 [i]
- linear OA(51, 10, F5, 1) (dual of [10, 9, 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(543, 390636, F5, 7) (dual of [390636, 390593, 8]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(542, 351016, F5, 2, 7) (dual of [(351016, 2), 701990, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(542, 351016, F5, 3, 7) (dual of [(351016, 3), 1053006, 8]-NRT-code) | [i] | ||
| 4 | Digital (35, 42, 351016)-net over F5 | [i] | ||
| 5 | Linear OA(543, 390637, F5, 7) (dual of [390637, 390594, 8]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(542, 195317, F5, 2, 7) (dual of [(195317, 2), 390592, 8]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(542, 130211, F5, 7, 7) (dual of [(130211, 7), 911435, 8]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |