Information on Result #1310503
Linear OA(561, 800, F5, 17) (dual of [800, 739, 18]-code), using 163 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 1, 6 times 0, 1, 13 times 0, 1, 27 times 0, 1, 45 times 0, 1, 63 times 0) based on linear OA(553, 629, F5, 17) (dual of [629, 576, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(553, 625, F5, 17) (dual of [625, 572, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(549, 625, F5, 16) (dual of [625, 576, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(561, 800, F5, 2, 17) (dual of [(800, 2), 1539, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(561, 800, F5, 3, 17) (dual of [(800, 3), 2339, 18]-NRT-code) | [i] | ||
| 3 | Digital (44, 61, 800)-net over F5 | [i] | ||
| 4 | Linear OOA(561, 400, F5, 2, 17) (dual of [(400, 2), 739, 18]-NRT-code) | [i] | OOA Folding | |