Information on Result #682861
Linear OA(542, 15649, F5, 8) (dual of [15649, 15607, 9]-code), using construction XX applied to Ce(7) ⊂ Ce(3) ⊂ Ce(2) based on
- linear OA(537, 15625, F5, 8) (dual of [15625, 15588, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(519, 15625, F5, 4) (dual of [15625, 15606, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(513, 15625, F5, 3) (dual of [15625, 15612, 4]-code or 15625-cap in PG(12,5)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(54, 23, F5, 3) (dual of [23, 19, 4]-code or 23-cap in PG(3,5)), 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(542, 15649, F5, 2, 8) (dual of [(15649, 2), 31256, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(542, 15649, F5, 3, 8) (dual of [(15649, 3), 46905, 9]-NRT-code) | [i] | ||
| 3 | Digital (34, 42, 15649)-net over F5 | [i] | ||
| 4 | Linear OOA(542, 7824, F5, 2, 8) (dual of [(7824, 2), 15606, 9]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(542, 5216, F5, 3, 8) (dual of [(5216, 3), 15606, 9]-NRT-code) | [i] | ||