Information on Result #682807
Linear OA(5114, 15649, F5, 23) (dual of [15649, 15535, 24]-code), using construction XX applied to Ce(22) ⊂ Ce(18) ⊂ Ce(17) based on
- 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(591, 15625, F5, 19) (dual of [15625, 15534, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(585, 15625, F5, 18) (dual of [15625, 15540, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(5114, 12504, F5, 2, 23) (dual of [(12504, 2), 24894, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5114, 12504, F5, 3, 23) (dual of [(12504, 3), 37398, 24]-NRT-code) | [i] | ||
| 3 | Digital (91, 114, 12504)-net over F5 | [i] | ||
| 4 | Linear OOA(5114, 7824, F5, 2, 23) (dual of [(7824, 2), 15534, 24]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5114, 5216, F5, 3, 23) (dual of [(5216, 3), 15534, 24]-NRT-code) | [i] | ||