Information on Result #1310320
Linear OA(519, 633, F5, 6) (dual of [633, 614, 7]-code), using 2 step Varšamov–Edel lengthening with (ri) = (1, 0) based on linear OA(518, 630, F5, 6) (dual of [630, 612, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(3) [i] based on
- 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(513, 625, F5, 4) (dual of [625, 612, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [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(519, 633, F5, 2, 6) (dual of [(633, 2), 1247, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(519, 633, F5, 3, 6) (dual of [(633, 3), 1880, 7]-NRT-code) | [i] | ||
| 3 | Digital (13, 19, 633)-net over F5 | [i] | ||