Information on Result #682794
Linear OA(5123, 15634, F5, 26) (dual of [15634, 15511, 27]-code), using construction XX applied to Ce(25) ⊂ Ce(23) ⊂ Ce(22) based on
- 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(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(51, 8, F5, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(5123, 8741, F5, 2, 26) (dual of [(8741, 2), 17359, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5123, 8741, F5, 3, 26) (dual of [(8741, 3), 26100, 27]-NRT-code) | [i] | ||
| 3 | Digital (97, 123, 8741)-net over F5 | [i] | ||
| 4 | Linear OOA(5123, 7817, F5, 2, 26) (dual of [(7817, 2), 15511, 27]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5123, 5211, F5, 3, 26) (dual of [(5211, 3), 15510, 27]-NRT-code) | [i] | ||