Information on Result #682789
Linear OA(5129, 15634, F5, 27) (dual of [15634, 15505, 28]-code), using construction XX applied to Ce(26) ⊂ Ce(25) ⊂ Ce(23) based on
- 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(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(50, 7, F5, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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(5129, 9627, F5, 2, 27) (dual of [(9627, 2), 19125, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5129, 9627, F5, 3, 27) (dual of [(9627, 3), 28752, 28]-NRT-code) | [i] | ||
| 3 | Digital (102, 129, 9627)-net over F5 | [i] | ||
| 4 | Linear OOA(5129, 7817, F5, 2, 27) (dual of [(7817, 2), 15505, 28]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5129, 5211, F5, 3, 27) (dual of [(5211, 3), 15504, 28]-NRT-code) | [i] | ||