Information on Result #682803
Linear OA(5120, 15649, F5, 24) (dual of [15649, 15529, 25]-code), using construction XX applied to Ce(23) ⊂ Ce(20) ⊂ Ce(18) based on
- 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(597, 15625, F5, 21) (dual of [15625, 15528, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(53, 22, F5, 2) (dual of [22, 19, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- linear OA(51, 2, F5, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [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(5120, 13649, F5, 2, 24) (dual of [(13649, 2), 27178, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5120, 13649, F5, 3, 24) (dual of [(13649, 3), 40827, 25]-NRT-code) | [i] | ||
| 3 | Digital (96, 120, 13649)-net over F5 | [i] | ||
| 4 | Linear OOA(5120, 5216, F5, 3, 24) (dual of [(5216, 3), 15528, 25]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5120, 1304, F5, 24, 24) (dual of [(1304, 24), 31176, 25]-NRT-code) | [i] | OA Folding and Stacking | |