Information on Result #1310394
Linear OA(541, 651, F5, 12) (dual of [651, 610, 13]-code), using 18 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 4 times 0, 1, 10 times 0) based on linear OA(537, 629, F5, 12) (dual of [629, 592, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(537, 625, F5, 12) (dual of [625, 588, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(533, 625, F5, 11) (dual of [625, 592, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(50, 4, F5, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-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(541, 651, F5, 2, 12) (dual of [(651, 2), 1261, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(541, 651, F5, 3, 12) (dual of [(651, 3), 1912, 13]-NRT-code) | [i] | ||
| 3 | Digital (29, 41, 651)-net over F5 | [i] | ||
| 4 | Linear OOA(541, 325, F5, 2, 12) (dual of [(325, 2), 609, 13]-NRT-code) | [i] | OOA Folding | |