Information on Result #682778
Linear OA(5150, 15649, F5, 31) (dual of [15649, 15499, 32]-code), using construction XX applied to Ce(30) ⊂ Ce(26) ⊂ Ce(25) based on
- linear OA(5145, 15625, F5, 31) (dual of [15625, 15480, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- 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(5121, 15625, F5, 26) (dual of [15625, 15504, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(5150, 11364, F5, 2, 31) (dual of [(11364, 2), 22578, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5150, 11364, F5, 3, 31) (dual of [(11364, 3), 33942, 32]-NRT-code) | [i] | ||
| 3 | Digital (119, 150, 11364)-net over F5 | [i] | ||
| 4 | Linear OOA(5150, 7824, F5, 2, 31) (dual of [(7824, 2), 15498, 32]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5150, 5216, F5, 3, 31) (dual of [(5216, 3), 15498, 32]-NRT-code) | [i] | ||