Information on Result #682787
Linear OA(5138, 15649, F5, 28) (dual of [15649, 15511, 29]-code), using construction XX applied to Ce(27) ⊂ Ce(23) ⊂ Ce(22) based on
- linear OA(5133, 15625, F5, 28) (dual of [15625, 15492, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(5115, 15625, F5, 24) (dual of [15625, 15510, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [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(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(5138, 12695, F5, 2, 28) (dual of [(12695, 2), 25252, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5138, 12695, F5, 3, 28) (dual of [(12695, 3), 37947, 29]-NRT-code) | [i] | ||
| 3 | Digital (110, 138, 12695)-net over F5 | [i] | ||
| 4 | Linear OOA(5138, 7824, F5, 2, 28) (dual of [(7824, 2), 15510, 29]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5138, 5216, F5, 3, 28) (dual of [(5216, 3), 15510, 29]-NRT-code) | [i] | ||