Information on Result #683846
Linear OA(547, 636, F5, 14) (dual of [636, 589, 15]-code), using construction XX applied to Ce(13) ⊂ Ce(11) ⊂ Ce(10) based on
- linear OA(545, 625, F5, 14) (dual of [625, 580, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- 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(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
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
Mode: Constructive and 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(547, 624, F5, 2, 14) (dual of [(624, 2), 1201, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(547, 624, F5, 3, 14) (dual of [(624, 3), 1825, 15]-NRT-code) | [i] | ||
| 3 | Digital (33, 47, 624)-net over F5 | [i] | ||