Information on Result #1310335
Linear OA(527, 640, F5, 8) (dual of [640, 613, 9]-code), using 4 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 0) based on linear OA(526, 635, F5, 8) (dual of [635, 609, 9]-code), using
- construction X4 applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(525, 625, F5, 8) (dual of [625, 600, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(517, 625, F5, 6) (dual of [625, 608, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, 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: 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(527, 640, F5, 2, 8) (dual of [(640, 2), 1253, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(527, 640, F5, 3, 8) (dual of [(640, 3), 1893, 9]-NRT-code) | [i] | ||
| 3 | Digital (19, 27, 640)-net over F5 | [i] | ||
| 4 | Linear OOA(527, 320, F5, 2, 8) (dual of [(320, 2), 613, 9]-NRT-code) | [i] | OOA Folding | |