Information on Result #682792
Linear OA(5132, 15649, F5, 27) (dual of [15649, 15517, 28]-code), using construction XX applied to Ce(26) ⊂ Ce(22) ⊂ Ce(21) based on
- linear OA(5127, 15625, F5, 27) (dual of [15625, 15498, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(5109, 15625, F5, 23) (dual of [15625, 15516, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(5103, 15625, F5, 22) (dual of [15625, 15522, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(5132, 11682, F5, 2, 27) (dual of [(11682, 2), 23232, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5132, 11682, F5, 3, 27) (dual of [(11682, 3), 34914, 28]-NRT-code) | [i] | ||
| 3 | Digital (105, 132, 11682)-net over F5 | [i] | ||
| 4 | Linear OOA(5132, 7824, F5, 2, 27) (dual of [(7824, 2), 15516, 28]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5132, 5216, F5, 3, 27) (dual of [(5216, 3), 15516, 28]-NRT-code) | [i] | ||