Information on Result #1310620
Linear OA(570, 651, F5, 21) (dual of [651, 581, 22]-code), using 17 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 4 times 0, 1, 9 times 0) based on linear OA(566, 630, F5, 21) (dual of [630, 564, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(18) [i] based on
- linear OA(565, 625, F5, 21) (dual of [625, 560, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(561, 625, F5, 19) (dual of [625, 564, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(51, 5, F5, 1) (dual of [5, 4, 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(570, 651, F5, 2, 21) (dual of [(651, 2), 1232, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(570, 651, F5, 3, 21) (dual of [(651, 3), 1883, 22]-NRT-code) | [i] | ||
| 3 | Digital (49, 70, 651)-net over F5 | [i] | ||
| 4 | Linear OOA(570, 325, F5, 2, 21) (dual of [(325, 2), 580, 22]-NRT-code) | [i] | OOA Folding | |